I would think 13 but I can't find it in the Bible what the exact age is. 20 seems to be the age that God wanted his soldiers in the army.
Some churches talk about this but are vague on what the age is. It's either this or 'confirmation' or 'first communion' but since I didn't go to church when I was younger I missed out on all this.
Also is it different for boys and girls. Or the same?
This can be a com plicated question. Part of the problem is, just what is 'Sin". It is a violation of "the law", but what law? God gave a command to Adam not to eat of the fruit of the specific tree or he would die. Now was the commandment due to God's will or was it given to prevent Adam from making a mistake with consequences that God could not undo without violating the purpose of creation?
If a parent tells their small child not to poke their finger into the hole in the ground that bees are flying in and out of, it is a command from the parent. The purpose though is not to enforce the parent's will, but to prevent harm that the parent can do nothing to stop. Disobedience by the child will result in a punishment, the bees will see to that, not the parent, but afterwards all the parent can do is to try to mitigate the suffering.
As for Adam, we do not know if he would have physically died even if he did not eat of the fruit, scripture does not tell us. Study of fossils though strongly suggests that even if Adam had not eaten, he would have physically died. But if the death was spiritual death, then it is plausible that Adam did die upon eating the fruit, and what lived on in Adam's body was not the Adam that God created.
Now for the individual, an infant does not seem to be aware that it is a distinct, separate entity. It knows that there is discomfort at times, but it also soon learns that the familiar "other" makes discomfort vanish so when the "other" appears it is a time of rejoicing and forgetting the discomfort. This can even be an unfamiliar "other" in some cases where the infant has learned that an "other" means comfort. When held by a parent who is upset or worried, the infant cries unconsolably, yet when handed to a calm "other", even if unknown to the infant, crying rapidly ceases until returned to the baffled, and still upset, parent. The infant, not seeing themselves as separate, mirrors the emotions of the person holding them.
Then, around age 7 months, the infant discovers their hands and that these hands, which can be controlled, can change the environment, the infant discovers that they can be independent of the environment. This is a delightful discovery, until the infant awakes in the middle of the night and it is dark, the infant is alone, and who knows what is in the darkness that cannot be controlled. The infant then begins to cry and scream, refusing to easily be comforted, especially by a parent who just wants the infant quiet so they can go back to bed themselves. Eventually this phase passes, but the sense of separateness will remain for the rest of the infant's life and will dictate their actions in large part for the rest of their lives. Once they, we, learn that we are separable, we must defend that separate entity, even at the cost of the real self that was created by God and interconnected with the rest of creation and God, and that protection will last until after the physical death of the person at which point, hopefully, the true self can regain control, rerecognize that they are interconnected with the rest of creation and God, and reject the false self and allow it to continue on by itself to its logical conclusion, total death as it has nothing left to feed upon given its separation from the true life of interconnectedness.
God does not enact the punishment rather the punishment is a logical consequence of our false belief and exacted by that false belief. Jesus pays the price for our sin, not because God needs a price paid, but because our false belief does. The parent, if allowed, will pay the price for the small child's disobedience in sticking their finger in the hole in the ground by addressing the bees, but how the child interprets all the actions does not necessarily fit with reality.
