Can a teacher video recorder a under age student without parent permission?

Yes. In my school there are monitors in the hallways and the hallways are video taped during and after school no permission was needed to have the school do this. Some teachers also tape their classrooms for various teaching projects or credentials and permission is not asked for by the teacher or the school before it is done. This is all school related, of course.

Yes the teacher is aloud to do this however they may not put the video onlinel.