Using real placenames

I've done both, using real and making up places. Each has its advantages. Made up places let you do what you want, and nobody can say "Silly! State and Main streets run parallel and don't cross!" However, it's sometimes harder for a reader (for me, anyway) to connect to a fully made up place. Often times, however, using a real place has opened up story possibilities once I found out more about it. Visiting real Nashville made my story Nashville more lively than if I had used a made-up Southern city.

I wouldn't worry about offending anyone, unless you go out of your way to use real people in the story.

Use the real name. Just changing the name won't stop readers from knowing where you mean. You'd have to change the location, and everything else, and then what's the point? There's a reason you're using Cuba as a setting, so use Cuba as a setting.

Given your scenario, I don't see why you wouldn't use Cuba as your setting. Real places are used all the time, represented for good or for ill. Go with what makes sense for the story.