First of all congrats on your first boyfriend.
1. If his mom thinks your a distraction from school, show her that you know how important school is. Set up study dates and yes, you really do have to study when you say you are. Not all of your dates have to involve school, but show her that you are a good influence. Once she gets the picture you can dial it down.

2. Ok, so people think he should be with someone else. Oh well, he's with you and that's all there is to it. You really like him, right? Ok then what people say doesn't matter. If they don't like it oh well, sucks for them because they have to deal with it. Be happy and know that you were meant to be together otherwise it wouldn't have happened.

3. Your friend has probably moved on if she has another boyfriend so you shouldn't have to worry about that. If she still has feelings for him (I seriously doubt it) then that's that, but if she takes it out on you then that says more about her then you doesn't it?
Hope this helped. Good luck