Yes they do allow for room charges on food, beverages and other incidentals. There is a small ATM on the property, but more services can be found if you take the short walk down Airport Road. There is also a nice little restaurant down off Airport Road called Josie's which is a great change for breakfast or lunch. And a market in that same area.
There was one ATM at this hotel. There were others I saw in the downtown area as well. I used my credit card at most places, cash for taxis. I believe you have to give them a credit card to reserve the room and they will put all charges to your room on that card. Not sure if you can change the card before you check out, you should call to make sure.
The bar restaurant uses the resort kitchen and serves some decent bar food. The restaurant which requires shoes is a sit down food is good. To help keep expenses down watch your alcohol consumption try to bring in your favorite treats. Keep in mind you are on a island and all is fair game when it comes to saving money
There is a couple little shops and I think one sold some beer but not sure. There is a great bar though and it was not expensive. You could always hop in a taxi and go to the grocery store that is not too far. Just depends what you're looking for and how much you are buying. If you just want a 6 pack then not worth the taxi ride.