one safety bottle for 2 or 3 students?
Are they supposed to bring one on post class dives too?
One per team. Yes.
Would also add the traditional method of making instructors-intern then institute by your peers.
Absolutely. I've been debating about categorically turning away intro students with a PADI Cavern card because of the "self-certification" path to become a PADI Cavern instructor -- I'm not there yet, but I definitely have a conversation that begins with "who was your cavern instructor" and based on the answer have told a couple of people that they need to audit my cavern course (no charge).