StinkyPantz- I think you got everything. Oh and isn't there a scripture somewhere that says that god doesn't require that children pay for the sins of their father (in this case Adam)?
In fact there is, don't remember exactly where in scripture, but I know that the law says that the age 12 and under they are not accountable for what they do. It's called "The Age of Accountability".
The reason for that is that children 12 and under who are not yet fully developed in the stages of puberty where the law of adultry and fornination doesn't apply to them. God cannot apply 9 commandments to a child and leave out one law. It doesn't work that way.
The ten commandments is structured together say like a puzzle and if one piece is missing then the ten commandments falls apart, so it's all or nothing.
So if a child at the age of 12 and under were suddenly to die, they will go to heaven automatically. Unless they reach the age of 13 where it's common for the stages of puberty to be complete and most 13 years may start being sexually active. But if I know my biology correctly, most of their sex drives don't become "full blown" until around the age range of 14 to 16. I could be all wrong since I'm not that good at biology, LOL.
Hope that makes any sense.
Yizuman