Things teachers are NOT legally allowed to do (things you can actually SUE THEM FOR):
1) Taking your things without reasonable cause (because you were texting in class does NOT count as reasonable cause, for example.)
2) Forcing you to stay after school (After school is done, you can leave no matter what they say and they can't do a damn thing about it)
3) Looking in your locker without reasonable cause
4) Physical punishment
5) Harassment (if the teachers are bullying you constantly, you can get them fired. I'm not kidding.)
6) Invasion of privacy (again unless there is reasonable cause, thanks for reminding me, maroon)
Teachers are literally powerless, don't put up with any of the things listed above. If they do any of those things, take some loving action.
I've gone and numbered your list.
1) They can stop you from doing nearly anything as long as it was disruptive to the learning environment.
2) They will usually just keep track of the times you skip on this and then get your parents and potentially the police involve. The police and your parents can force you to stay after school.
3) The term you are looking for is reasonable suspicion.
4) This varies from state to state.
5) You are correct. But usually they will just get a warning and wise up. Also, have fun trying to prove harassment in court.
6) Once again, reasonable suspicion.