We usually say "мальчик" about a child (male child, of course). Teenager of 12-16 is usually called "подросток". An older boy is "парень". Age bounds I have put here are not strict, of course, but just approximate.

I think the difference between "мальчик" and "парень" is the same as between English words "a boy" and "a guy". Basically, if he is under thirteen, he is a "мальчик", after that he is a "парень". Although sometimes people also can refer to young men as "мальчики", just like in English people can call them "boys".

Yes. "Мальчик" is a child, "парень" is a young man. But sometimes little boy we can call "парень" if want to show that he is clever, and say "мальчик" when speak about yong man, if he is very young (for example, a woman can say "мальчик" about her young lover).