It would be the Amerindians that lived in Cuba prior to Spanish colonization.
There was an excellent article on this — the Taino — in Smithsonian Magazine, about seven years ago. Quick answer: No, a few thousand people near the east end still have a few Taino culture traits and partial genetic ancestry.
No. It was Tainos. They disappeared because they were worked to death. Literally.
The Spanish began importing African slaves because (a) there was a ready supply, the coastal Africans would happily sell their captured interior neighbours, and more importantly (b) the local natives died off from being used as slaves.
One item about the slave trade I read said a Caribbean island slave was lucky to last 5 years. Fortunately (?) there was a steady supply from Africa. Presumably any locals wanting to survive would have to disappear into the jungle - this was probably easier on the mainland than on smaller islands. Over time any discovered tribes would be captured and put to work (to death) and their hideout range became smaller and smaller… nowhere to run.
More likely from contracting diseases against which they did not have immunity.