Do you think I have a good chance of getting into Harvard College?

[skieurope]

Do I have an advantage over local US citizens because I was born in a Caribbean island?

No. The international acceptance rate is about half the overall rate.

I am planning to take the ACT (with writing) or the SAT (with 2 subject tests) four subsequent times before applying to universities in the USA

That should not be a goal. If you get 34/2250+ the first time around, call it a day and move on.