Murder is a felonious offence. Only one sentence can be passed on conviction of a felony; that is, capital punishment, and therefore John Edwards must be sentenced to be hung by his neck until he is dead, hanging being the only available method of execution.
That John Edwards is a young child is of no bar to his being executed: the age of criminal responsibility is 7.  Children are regularly indicted and convicted of felonies and must suffer the consequences under the law as adults do. Blackstone's Commentaries records one such occurrence:
"â€¦ a boy of 10 years old was convicted on his own confession of murdering his bedfellow; â€¦ it was unanimously agreed by all the judges that he was a proper subject of capital punishment." 
This account most likely refers to the case of William York who stabbed the young girl he shared a bed with, Susan Matthew (aged 5) in the institution where they resided. He was duly sentenced to death. 
There is no discretion available in the case of murder; the death sentence is mandatory, and universally applied. The reason for this is that it is one of the most heinous crimes that can be committed. Children are not spared the rope, because the judiciary considers that treating them differently "might be of dangerous consequence to the public, by propagating a notion that children might commit such atrocious crimes with impunity."  This coalesces with the general view of the period that children are not especially vulnerable or deserving of more sensitive treatment than adults.
However, despite the mandatory passing of this sentence, less than 2/3 of those condemned to death are ever executed.  This is because the stricture and cruelty of the 'bloody code'  acts in conjunction with the merciful possibility of a royal pardon. Every case where a capital sentence passed is reviewed by the monarch. To decide whether to grant a pardon they consider the circumstances of the crime and the character of the convicted. In the early nineteenth century the proportion of condemned criminals who received a pardon rose to a staggering 90%, and by the 1830s peaked at 97%.  There are strong reasons for supporting the pardon as an adjunct to the sentence of death. The possibility that the crown could grant a conditional pardon, which commutes the sentence, or even a free pardon, which allows the convicted criminal to walk free, achieves several aims: it gives the monarchy total power of life and death over their citizens; it mitigates against the severe judgment of death which necessarily has to be pronounced; it enables the state to appear paternalistic and merciful; and, it achieves the aim of keeping sentencing unpredictable and subjects fearful of the monarch's rule.
When passing sentence on John Edwards it would be well known that a pardon is likely to follow because of his young age; public records of juveniles hanged in the nineteenth century show less than a handful who were under the age of 14. One, William Jennings, who was hanged at Chelmsford for arson on 5th August 1831 was reported to be aged 9, but it is widely accepted that this seems unfeasible, and he was most likely 19.  In fact, sources suggest that John Bell, aged 13, executed on 1st August 1831 in Norwich for the murder of 13 year-old Richard Taylor was most likely the youngest person to be hanged in the nineteenth century.  Mid-nineteenth century, public opinion has deserted capital punishment. The number of felonies for which it is a standard sentence has been substantially reduced, and it has become reserved for the most heinous of crimes.  Child murderers are not viewed as so heinous as to be deserving of this punishment, and in almost all cases a royal pardon will be granted. This was so in the case of William York,  even though his crime was particularly violent and his character particularly detestable.
If John Edwards were granted a pardon, his sentence for would be commuted either to transportation,  preceded by a term of imprisonment in a penitentiary institution  or reformatory school.  The reason for this is that these are the most appropriate punishments, offering an opportunity for him to be dissuaded from entering into a life of crime before removing him wholly from society.
Murder is multi-offensive; being committed firstly against the individual by the wrong inflicted, secondly committed against the king by disobedience to the laws of the land, and finally committed against the public by setting an "evil example."  Punishing this crime by death ensures that all three wrongs are addressed. This is because capital punishment serves two, equally important aims: first, execution completely and irrevocably incapacitates the offender; and second, public execution deters criminal behaviour by proving to citizens that law-breakers will be dealt with seriously and harshly.
The success of executions deterrent effect comes from cultivating a climate of fear. England's penal philosophy was originally founded on the infliction of painful physical punishment. The pain is in itself a punishment. Indeed, most condemned men slowly strangle to death by the short drop from the noose and writhe in pain for some time. More importantly, however, the pain is instrumental. Fear of the pain "inspire[s] terror in those whose duty it [is] to obey."  Collective terror makes the King's subjects as a whole fearful of the consequences of disobeying of the laws of the land and thereby upholds social order. This is the reason that the singular sentence of death was utilised for so vast a range of crimes.
This fear is exacerbated by inflicting the punishment before a crowd:
"[the] evocative, disciplinary power relie[s] on the theatrical and public infliction of pain and physical harm for [its] moral and punitive effect â€¦ sham[ing] and humiliat[ing] offenders before their community and reassert[ing] the power of the state." 
Public executions remind citizens of the pain they will suffer on breaking the law. In an era without an effective police force and when crime is rife, this reminder is necessary to maintain public order.
However, due to the 'bloody code' making almost all felonies punishable by death, executions had been becoming more and more frequent in the mid-1800s. This has led to a problem: rather than being appalled by the horror, "spectators [are] overwhelmed by the carnage,"  especially since so many young children are being hung. By the 1840s the public spectacle of parading the condemned to a place of execution had been abolished, it being realised that this was merely only inciting public disturbance. Erecting gallows just outside the prison gates was designed to "expedite death [and] limit the interaction between victim and executioner,"  but a public gallery was retained as a continued reminder. The suffering of the condemned was considerably reduced, but the punishment remained in place. Incapacitation was still served, and it was the spectacle and not the execution itself which was undermining deterrence. If anything, the sanitised arrangements likely increased the fear as it was no longer an enjoyable event for the crowd, but a clinical dispatch.
In addition, the possibility of pardons offered hope for a reprieve. This uncertainty operated to intensify fear of the monarch, who has ultimate authority to decide if the condemned lives or dies, and adds to the effectiveness of capital punishment in deterring criminals.
(a) Two crimes have been committed here by two separate offenders. I would sentence each defendant to a term of imprisonment for the theft from their master, commensurate with the value of the items stolen (provided neither had a previous record of theft). I would further sentence Kate Moss to 7 years transportation to Australia for the arson, and sentence Davy Williams to 10 years transportation for the same under the Transportation Act 1718.
(b) The policy reason behind passing sentences of imprisonment and transportation in these cases stems from an increasing public unease at criminals being hanged for so many minor crimes. Physical punishment had formerly been the cornerstone of sentencing, but greater use was now being made of punishments which not only incapacitated and deterred, but also reformed criminals and put them to work. Punishment was changing from a single event to a process of "disciplining the soul of the offender."  This shift in philosophy can be summed up as follows:
"The body now serves as an instrument or intermediary: if one intervenes upon it to imprison it, or to make it work, it is in order to deprive the individual of a liberty that is regarded both as a right and as a property." 
Deprivation of liberty, rather than "brutality and cruelty, which in former times had been thought to intensify the sting of correction, [but] were [now] seen as excessive and incongruous,"  is the new cornerstone of sentencing theory. Imprisonment and transportation are sentences which the potential criminal will dread, without being wholly abhorrent to principles of morality, and in which the public can place their trust. They are not a pure demonstration of the overwhelming power of the state, but directed toward changing offenders into productive members of society. 
Imprisonment is the appropriate punishment for the crime of theft from one's master (a statutory offence created in 1823 in response to increasing concern about the behaviour of workers  ).
The crime of arson is particularly suited to transportation. It is a common law crime, defined by William Blackstone as "the malicious and wilful burning of a house or outhouse of another man."  The primary wrong committed therefore is against the security of habitation; it is not seen as a crime against property, rather as a crime against the public.  Because of this arson is considered to "evidence a moral recklessness and depravity in the perpetrator,"  and therefore demands a serious and lengthy sentence. Transportation is befitting because it is a more severe punishment than imprisonment, exiling the individual to a distant land where the conditions are rough and few survive the journey out let alone live to return to England upon completion of their term.
A particular benefit of both imprisonment and transportation is that punishment can be meted out in accordance with the particular circumstances of the crime to a level befitting the actual criminal action undertaken (although in the case of transportation standard length sentences were common). An appropriate sentence is reached by considering similar decided cases:
In relation to the theft the following similar cases give some guidance as to what appropriate sentence levels would be once the value of property stolen is known: Joseph Vowell (age 17) was confined for two years having pleaded guilty to stealing various items of property belonging to his masters, which amounted to the sum of 31 sovereigns, 22 half-crowns, 11 shillings and sixpence.  Walter Sallis (32) was found guilty of stealing a small amount of money from his master. He was strongly recommended to mercy because of his good character, and was sentenced to be confined for three months.  Mary Lawrence (40) stole a sheet, value 3 shillings. from her master. Upon pleading guilty she was sentenced to be confined for six weeks.  If any of these had had a previous conviction they would not have been imprisoned, but transported.
The following cases were of assistance in determining the periods of transportation set above: Mary Jane Fitzgerald (25) was transported for 7 years in 1848 for "feloniously setting fire to a house in the possession of Emma Beaumont, with intent to injure,"  and James Ragan (28), who in 1850 "feloniously set fire to a certain building belonging to Norman M'Leod and others, with intent to injure them" was transported for 10 years. 
It is acceptable for Kate Moss's sentence to be of a shorter length than her co-defendant, since women are regarded as being less criminal than men, and subject to forces and influences which they need to be protected from. 
Transportation achieves many aims of punishment: firstly, it solves the problem of overcrowding of gaols and provides substitutes for the lack of workers in the colonies;  secondly, it potentially leads to the reformation of the offender, giving them time to dwell on changing their ways; thirdly, fear of being sent to unknown circumstances in remote areas of foreign climes may act as a deterrent; and fourthly, if all else fails it is "a [simple] means of ridding the country of the idle and incorrigible;"  and, since there is no established procedure for return to these shores once the sentence has expired,  it acts to directly reduce the crime rate.
As of the Penal Servitude Acts 1853 and 1857 transportation is being faded out and substituted by a new system of penal servitude. If Kate and Davy were convicted right at the end of the 1850s this would probably be the sentence passed upon them, although they may still be transported rather than serving their time in an English prison because of the gradual and unclear change-over. Penal servitude began in response to the concern that "the good lodging, good food and plenty of sleep which convicts enjoyed [in prison] â€¦ went far to balance their loss of liberty, and abstinence from women, spirits and tobacco."  Putting convicts to work could either act as a deterrent, by requiring hard manual labour, or provide a convict with industrial skills which he could utilise on his release for the good of society.
Imprisonment serves the aims of reformation and rehabilitation well. Prior to 1819, prisons were only occupied by debtors or those awaiting trial. But the great period of reform and building of new institutions dramatically changed the usage and purpose of prisons. They turned from "chaotic, unregulated, disorderly places of detention"  to "recognizably modern institutions, systematic and purposeful."  Indeed, prisons were "developed with the â€¦ 'criminal class' in mind"  and with the core focus being hard work, religion, and promoting the rightful positions of criminals in the natural order of society.  . One particular prison, the Panopticon, designed by Jeremy Bentham, allowed all prisoners to be observed without knowing if they were observed or not. The beneficial effect of a design with "lateral invisibility"  was that it was "a guarantee of order â€¦ there is no danger of a plot, an attempt at collective escape, the planning of new crimes for the future [or] bad reciprocal influences." 
Attempting to kill the Queen amounts to High Treason.  Under the Treason Act 1814, Robin Loxley must therefore either be hung and posthumously quartered, or, if the King so authorise, be beheaded.
However, as he is only 25, if they jury were to recommend him to mercy, I would be minded to follow the case of George Mullins (22) who was convicted of treason but transported for life in 1848 on account of his youthful age. 
The common law also requires the guilty person to undergo 'forfeiture,' forcing them to surrender all their lands and property to the state, and their immediate family and hereditary heirs must be subject to 'corruption of blood,' which prevents them from owning property, conducting business or inheriting anything from the guilty party. 
Treason law originated in attempting to safeguard a state based on Kingship which was first established during the reign of Edward III.  Treason amounted to a betrayal of loyalty and threatened the security of the state; it therefore merited disciplinary action far in excess of that justified for any other crime. The gruesome punishment dictated under the Statute of Treasons 1350 was designed to keep civil disorder to a minimum, and the four parts of the body were traditionally sent to the corners of the realm to deter all citizens from following similar schemes, and to prevent the guilty man from entering the afterlife intact. The unique infliction of punishment beyond the perpetrator took place because relatives were tainted by the traitor. Stripping them of their lands and inheritance would effectively ruin them, and thereby also act as a stark warning to any others who harboured thoughts of overthrowing the monarchy.
Depending on the actual action taken by Robin Loxley, this conviction could also in these days alternatively amount only to the lesser offence enacted by s.2 Treason Act 1842 of assaulting the Queen. This would make Robin Loxley guilty of a High Misdemeanour, and liable only for a minimum of seven years' transportation or three years' imprisonment with or without hard labour and whipping. If he used a firearm he would fit squarely within the realms of section 2, as in the case of William Hamilton (23), who was transported for 7 years for discharging a loaded pistol near Her Majesty Queen Victoria with the intent of alarming her. 
Full punishment was rarely ever carried out, it being considered so barbaric. The Cato Street conspirators were the final convicts to be sentenced to this grisly punishment in 1820, long before its eventual removal from the statute book in 1870, and even they were only beheaded.  The main aim of the sentence was deterrence, and indeed, it was enough of a deterrent that the elements comprising the punishment became such a part of the common vernacular; the grisly act of quartering the body did not need to actually take place.
The enactment of the lesser offence in s.2 was beneficial since it introduced the possibility of distinguishing between treasonous acts. It was enacted in response to several attempted assassinations of Queen Victoria where no harm was caused and enabled a merciful approach to be taken. How the actual sentence of imprisonment/transportation will achieve the aims of punishment has been considered above.