The answer to your questions is Yes. They will store your luggage until your transporation to the airport is ready.
Keep in mind they will schedule your transportation to the airport as least 4 hours prior to your flight.
Yes, definitely. We checked out at 11:00 in January. We were flying TimAir, so we didn't need to leave the resort until 12:45. That gave us time to stroll the beach, have lunch, and enjoy a few cocktails. No problem!