I think paintball guns and airsoft guns would make a good add-on. Also maybe knifes, and also at some point Jimmy (Or whatever character we follow) will obtain a gun. Now I realize it may sound to much right now, but I do think you should be able to kill people. However, afterwards a big police investigation will take place for multiple in-game days. If there was witnesses/clues then you can get busted. Otherwise you won't get busted. Also like GTA4's system, you could knock people out, and kill them if you kept attacking. What comes to mind though when you kill the students is they could all disappear right? A few ideas, new students could come to school OR they just recover later on, but it takes a few in-game days. Also when you go to the principals office you should have options on what to say. Make up excuses and lies. And change the punishment, have a detention period with multiple things to do.
1) Just sit and be normal for a little while
2) Throw paper balls/airplanes at people
3) Fake going to the bathroom and just sneak out
4) Get out when the teacher isn't looking.
On to another topic, authority figures are always hostile towards you it seems. Perhaps they're respect for you could shift based on how often you've been busted recently, grades, and attendance.
Also earlier I said you could kill, for big crimes such as that you should go to the juvenile detention center, get in fights there maybe. Have your parents or someone get you out, or sneak out.
Be able to take vehicles. No, not just skateboards and things, cars to.
The authority grabs you and you rapidly press a button to escape can stay, however they shouldn't continuously attempt to grab you if you keep hitting them.
Then one last thing, a bit of a small detail but still important. When using thumbs up, you just greeted. You should be able to get into more conversation rather then just saying "Hi" repeatedly.