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It's not legally binding, but is designed so you both have evidence of the agreement you made. This is usually in place of a more severe punishment. From my experience as a teacher, it is usually brought to the parents if you don't live up to your part of the agreement, so it does not sound like they are doing anything illegal or immoral, just trying to get you back on track.

First of all, the contracts you discuss are not legally binding. These contracts are used, however, as a written expression of the agreement that you and your teacher or principal are making. If you should violate the contract, the consequences are usually written in the contract so you know what to expect. It's actually a good thing. It's a clear way to show what is acceptable and what is unacceptable behavior. You are not forced to sign a contract; however, be advised that this shows that you are uncooperative and perhaps not wanting to admit you have a behavioral problem that needs to be addressed. From my experience, most students try to live and abide by the contract; it's a positive thing. For those who refuse to take part it, my experience has been that those students tend to get suspended (they continue to break school rules, show disrespect for authority, etc.); moreover, some of those students get expelled. Perhaps a healthy way to think of these contracts is to consider them a written promise on your part to change your behavior.

Sometimes teachers make behavior contracts with students. For example if the student does XYZ then the student will be rewarded with... This is not a legally binding contract. The only thing that happens if the student violates the contract is that the teacher will not reward the student. So, yes a student can sign a contract without a leagal guardian. I have used contracts before.

Signing a contract is a typical way that teachers and principals have of getting students to behave. Often a student will say that he/she did not understand. The purpose of the contract is to make sure the student does understand. You are right that it would not hold up in a court of law, but it would hold up in the future if you do what you say you will not do in the future. It will hold up with your parents at a parent conference if they question that you understood what was required of you. You do not have to sign it but you probably should as they could come up with something worse. Like calling your parents in with you and having you explain to the whole group what you have done and what you will do in the future.

The principal and the teachers run the school; you do what they say - period - end of story.

if you are 17yo or younger it's meaningless.

Minors may not enter into binding contracts.