Of course. Its a public site. Teachers are part of the public. ANYONE can look at your Facebook page unless you have to restricted. People get fired from jibs all the time because bosses look at Facebook pages and see stupid things. You kids dont seem to get that when you put something on these social sites ANYONE and EVERYONE can see it. Theres no such thing as 'private' on a public site unless you have restriction settings in place.
Maybe. If you're logging onto facebook from school, using their computers and internet connection, there's a good chance it's legal because students have less privacy rights at school. If you're at home and the teacher is gaining access through a stolen password or such, that could be less legal. I think the analogy would be something like going through your backpack or notebook.