That depends how sophisticated your school's system is.
If you have to log in to the network with your own username and password, the answer is probably yes. If everyone is using the same password to connect to wifi, then probably no.
Yes. Every school system wifi is monitored by the NSA, FBI, CIA, Homeland Security, and the state & local police.
Yes, easily tracked and identified! And then expelled for breaking the school rules.
Hopefully, yes. You're an idiot for even asking.
If their IT has half a brain, they block it, and trying will get your dumb *** expelled.
Yes, you will get caught