Hi, I sailed the Dream back in April. I can't answer all your questions, but I'll try.
1.) Can't really think of anything, sorry.
2.)They have a kids club you can put her in for the duration of the show and if she is attached at the hip and you still want to see it, it will be showing in your stateroom on your tv. You won't miss it, one way or another.
3.) Sounds like a good plan. It seems most people stayed on the ship at Nassau and at CC folks seem to come back to the ship early even though it was a pretty day when we sailed. We were still able to ride the Aqua Duck back to back with only a 3 min wait on that day because we did it before noon.
4.)Pirate night was the on the second night of our 3 night cruise. But, I would think it would be scheduled for Castaway Cay night on a 4 night- not sure though.
5.) One of the things I love about a Disney short cruise is their is NO formal night! You can wear jeans to dinner (no shorts please) and dress up as little or as much as you want. For instance the first night I wore jeans, for Enchanted Garden I wore a sweet little white cotton dress, for Animators and Royal Palace I wore white pants and a button down shirt.
6.) Another thing I love about Disney...pre-cruise fun! Create door magnets and your cruise will begin before you even sail. Make them for each night of your cruise if you want, i.e Pirate Night, Castaway Cay Day etc.
7.) No DVD players in the room, but they do play first run Disney animated and non-animated movies at the theater and the cabin shows Disney shows, ESPN and animated movies. No worries there!
AND THE KIDS FOOD IS AMAZING! I eat their mac n cheese, pizza, chicken fingers, Mickey Waffels etc.! Have fun and rebook onboard to save money!