IS THERE A STORE WHERE I CAN PURCHASE GROCERY ITEMS AND HALF BARREL RUM BY THE BOTTLE?

No, Caye Caulker is a dry area!

It's dry only on the land....yes there is Chan's where you can pick up some rum...beer etc. Not to worry. Wow i got scared there for a moment...lol

Caye Caulker has several markets. Chan's Mini arket is probably the largest with a little bit of everything, but there is also the Friendship Store on Front Street(snacks and beverages, including rum), J & L on Middle Street (general supplies, plus some produce and ice cream), other little markets are: Center Store aka Nachie's, Celies Store, and Albert's.