The thought that suicide is an unforgivable sin is not really Biblical, at least not directly. It is however based on something.

It was thought that someone who comitted suicide did so because they have lost all hope, and that no true believer could lose hope, becasue a true believer always had some hope from their faith. Thus only a person who was no longer a believer (or never was) could kill themselves. On top of that, this non-believer, no matter how sinless beforehand, died committing the sin of murder (of themselves) and so had no chance for a priest to grant absolution even if he changed his mind after it was too late.

So two false ideas led to this idea that suiside was a one-way ticket to hell. Fisrt, a true believer can lose hope in this world: "I can't take it anymore, I'm coming home! Forgive me for this Lord (stab)" Second, a priest is not needed for God to grant forgiveness. In fact, the Bible isn't even clear that we can't be forgiven after death. Not that I'd want to count on that, but still.

The Law of Love tells us here that there is hope that suicides of any age are not automatically thrown into the fire.

As to the "AoC" for sin, Biblically, one was not responsible for your sin until you became an adult. For girls, this was upon her first period, and for boys this was upon his Bar Mitzvah at 13.

In Christ,
~CSL