You are better off buying alcohol with a big mark up in Cancun (eg Vodka) at the duty free shop before you leave the US. Corona and XX are cheap in Mexico.
Yes, but the selection totally depends on the airport. Even if you can find some, I think it'd kind of dumb to carry beer from the airpot to your hotel when you can just get it from the XOXO convienent store near your hotel for probably the same price if not cheaper.
Basically When i get there I think i am going to stock up on bottles for the room.. So whoever is missing out on the action just look for me Ill make sure you get taken care of :