Teacher/Student privacy issue.?

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Okay, my friend is going through some trouble at school. I'm just curious to know a few things...
1. Are students and teachers allowed to be friends on facebook?
2. If a student and a teacher are not friends, are they allowed to attempt to view each others profiles a) without permission b) by going on someone else's account?
3. If a student has their profile set to private, does not have a teacher as a friend on facebook, and still the teacher manages to view their page, is this a violation of privacy?
4. Is a student allowed to be punished by a school for something that appears on facebook?

Any help you can give would be so greatly appreciated.