What is colloquial word for kind of punishment for children/teen when he's not allowed to leave home (go to friends etc), but only school-home-school... ?
You use an adjective grounded as it means:
(of a person, predicative) Confined to stay inside, typically by a parent, as a punishment.
1.1 informal (Of a parent) refuse to allow (a child) to go out socially as a punishment:
"You are grounded." means you are not allowed to go out to have fun.