Scuba diving for first time cruiser - Keys & Abacos

[hellosailor]

bear-
Lots of issues and you've gotten some fine responses on them. Whether you can anchor or moor will very much be a local issue, check noonsite.com and then check local authorities, or dive operators, to try confirming whether you can moor or anchor. Leaving your boat unmanned while you dive is probably legal, but a personal choice. Even in US waters, divers have had issues with their boat coming loose and going away. And of course you may need a large diver-down flag (varying) to fly while in the water.
Leaving a hang line off the boat, so you can doff your gear, tie it off, and haul it up after you are inboard, is easy enough to do. Also do join DAN and get their medevac insurance if you don't have that yet. Quite reasonable.
I'm not sure that you will be able to get your US tanks filled in all locations, because everyplace may not be allowed to fill DOT-certified tanks. Canada can't, and the EU can't, and if you're at an island which is perhaps French territory? They'll probably be bound by EU rules, although I'd expect many to ignore the point. If it looks like tank rental may be required...worse things happen. (Personally I hate rental tanks, because I prefer the larger new steel tanks, and a J valve, and that last one is simply not going to be found for rent.)