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I don't know about the Island Star but I'm pretty sure that duty free cigarettes will be available simply because there is profit to be made! However, it's usually much cheaper to buy them on land. Most ports have a duty free shop and I paid around 80p a pack last year in some places! Perhaps someone should start a thread: "Where have you found the cheapest cigarettes?" ;-) I actually saw some for less than 10p a pack in St Petersburg a few years ago...
Yes it has, although you may well be better off buying them from the very nice duty free shopping mall at Barbados port. You should have plenty of time to browse this area before sailing (which you have to pass through to go into the town). As far as smoking on the ship goes you have probably picked one of the smokiest ships that I have been on for years so you should have a good time!