I agree with "Dd's" advice on all 1-4, I can't belive they didn't make you buy your own snorkeling equipment to get certified! owning your own mask, fins and snorkel used to be a prerequisite to taking dive classes!
Don't be worried about being a slow desender, I've been diving for 20+ years and am usually the last one to the bottom. Just let the DM know you are a new diver and you are a slow clearer (is that a word?) and they should be patient with you. going to 60' plus is really no big deal, you've been to 35', the first 30' are the hardest. Most of the boat entries on Cozumel are frogman style, sitting on the side of the boat and rolling backwards into the water, if you can fall backwards you can do it, just pretend your Mike Nelson, (am I dating myself?) and go for it!
Stay close to the DM, relax and enjoy the ride, dift diving is really the easiest diving there is, it takes very little effort on your part unless you try and fight the current then your going to burn a lot of air and not enjoy it at all. Bouyancy is the key and you'll get better at that with experience and the only way to do that is to dive.
Personally I'm not a huge fan of getting one certification after another, experience, in my opion, is greater than another piece of paper and sitting in a classroom for a couple of days on your vacation. Get a few more dives under your belt before you spend any more money on certification classes. Don't they require you to have at least 15 dives before taking Advanced anyway? Spend the money on snorkeling eq. and wetsuit.
Hope you have a great trip, let us all know how it goes.