Do they accept a I'd from Dominican republic?

A Passport is required if you live outside of the US.

Don't know, but probably. They can't get your money if you're not on the boat

I'm not really sure but what you should be able to use is your passport, not your ID

I would think, because this is a tourist area, they are ok with that

I wouldn't know why not as long as it is legit and has a matching picture