Lucky you! A few days ago we went to Palancar Caves. We were the first boat to the site but certainly not the last. I would have to guess that we saw at least 150 divers pass us during the dive. Some were in large groups (there was probably more than one DM to maintain the requisite ration but they were all diving in a herd) and some were in smaller groups. They were above us and below us. Our DM finally just moved over to the shallows where we continued in peace.
Correct, but it never happened to me. They do not mix the groups (neither from different ops) for a matter of reciprocal respect. You can occasionally meet other groups, but you will never dive with dozen people from other groups.
Also, almost all the dives in Cozumel are drifts, a couple of minutes of separation is enough to get distance from other groups.