See this link, it should help(especially the Note section):
http://www.wtgonline.com/data/cym/cym040.asp
And make sure your parents' visa is Multi-entry so they can come back to the states.
2. Between Carnival and Royal Carribean, which one is better?
They are both owned by Carnival, so doesn't matter. What matters is which ship (newer ships are typically better) and what entertainments/activities are on board.
3. I heard that I should avoid windy season. When will that be?
Don't know about this one, sorry.