In the US, health insurance certainly is complicated. 

You will find many different opinions on what Medicare does and does not cover. 

My best read on traditional Medicare (Parts A and B) is that costs incurred in foreign countries will not be reimbursed, unless you live by the Canadian border and the Canadian hospital is closer than your US hospital. Will not apply for problems in the Caribbean and elsewhere.

Many Part C (Medicare Advantage) plans will reimburse you for foreign expenses. Check your plan.

I will defer to Eric on Plan F, I know nothing. I read up on it on the internet, and came away even more confused.