Cuba is a tyranny. They've soften up to get European investment and tourists, but they're brutal in their indoctrination, imprisonment of dissidents, etc. They're also an important (and beloved) backstop preventing American domination in L. America.
Pinochet didn't fall, he basically handed over power peacefully. His (surprisingly liberal) constitution of 1980 established him as head of the armed forces (which he was until he died) and promised free elections. He allowed for a fair and free elections in '88 that he lost and whose result he respected paving the way for the 1990 presidential elections. Again he lost and respected the result.
He's also a murderer who slaughtered thousands of innocents, but that's peanuts compared what the commies have wrought.
Everything I wrote is a gross oversimplification. Volumes have been written for each of the three topics you glibly referenced.