Hey Phil. :)
We believe:
Namely, that no bearer of burdens can bear the burden of another;
That man can have nothing but what he strives for;
That (the fruit of) his striving will soon come in sight:
Then will he be rewarded with a reward complete;
That to thy Lord is the final Goal;
(Qur'an Surah Najm [53] : 38-42)
If we strive to do good in this life, then we will be rewarded for that good, and if we do evil - nobody else will get the punishment for it - but instead, the one who did that evil will be punished for it.
The same way, if a person does a crime in this world - the one who does the evil should be the one who gets punished, not any innocent who wasn't even there to stop the crime.
But in islam if one repents sincerely (hoping not to go to that sin again), then Allaah Almighty can choose to forgive that person. That is easy for Allaah.
Therefore give admonition in case the admonition profits (the hearer).
The admonition will be received by those who fear (Allah):
But it will be avoided by those most unfortunate ones,
Who will enter the Great Fire,
In which they will then neither die nor live.
But those will prosper who purify themselves,
And glorify the name of their Guardian-Lord, and (lift their hearts) in prayer.
Nay (behold), ye prefer the life of this world;
But the Hereafter is better and more enduring.
And this is in the Books of the earliest (Revelation),-
The Books of Abraham and Moses.
(Qur'an Surah Al A'la [87] : 9-19)
Regarding the son of Adam who killed the other;
[فَطَوَّعَتْ لَهُ نَفْسُهُ قَتْلَ أَخِيهِ فَقَتَلَهُ فَأَصْبَحَ مِنَ الْخَـسِرِينَ
So the Nafs (self) of the other (latter one) encouraged him and made fair*seeming to him the murder of his brother; he murdered him and became one of the losers.
[Qur'an Al Ma'eeda 5: 30]
The children of Adam have the freedom of choice to go down the path of good or evil. This is why those who persist in evil follow their cheap carnal desires, whereas the believers are ordered to control their desires and channel them in a positive/permissible manner. I.e. instead of fornication, through marriage, instead of stealing, through earning through business transaction for example etc.
The word 'nafs' is used within that verse, and this is explained as the '
Id' in pyschology. The 'evil carnal nature' one can say, yet this nature can't force us to do evil - since we have the power to control ourselves from doing that.
The shaytaan (devil) can't force us to do anything, rather he whispers to us to make some evil seem attractive to us, so we incline to do evil, yet we have a freedom of choice on whether we will go ahead with that evil act or obey Allaah's commandments instead, and then get a good reward for that inshaa Allaah.
The whispers can increase one to desire the evil, and the nafs can either incline to that evil and get a cheap temporary pleasure, or it can turn away from it, and then get the pleasure of Allaah - tranquility in this life and the next, His Mercy and a great reward.
The son of Adam killed the other out of freedom of choice, he knew it was wrong - especially since killing was prohibited. But he inclined to evil and killed his brother, and therefore became of the losers. It wasn't related to the sin of his father since God forgave Adam and Eve when they sincerely repented to Him. And without a doubt, all the children of Adam would return to the Creator of all things on the Day of Judgement so justice can be settled.
In regard to the children being sinful or doing crazy things, then we know that a child by itself won't usually do evil and is sinless anyway. Yeah, it may play about or do things by mistake, however it won't steal a sweet for example since it will know that it's wrong - especially on it's first time.
Or in a culture where violence is the norm, the child at the beginning won't want to harm others, yet the society around this child may influence it to do this evil - so the child get's used to it, and therefore the fitrah is likely to have altered. However, as this child get's older, if he/she is sincere in searching for the truth, then they may find it and come to realise that it is a reflection of what they've been missing and searching for all this time.
And Allaah knows best.
Regards.