will the school find out that I used VPN to browse instagram in my school iPad even I delete the history of it?

Yes. Your school uses a proxy server to access the internet. Every request is logged. If they scan the logs, they can find out who used which computer and what their activity was. There is no way for you to access those logs and delete your transgressions.

All activity via VPN is also logged, which machines you interact with, and what your activity is on those machines.

Quite probably - Yes!
1. They may have some kind of hidden logger installed in the unit.
2. If you were using the school's internet connection, then it's possible that the iPad uses encryption keys from it's own server, so that even your https traffic becomes fully visible to them.

yes... they most likely have programs on the ipad that record all activity even if you used a vpn....

yes