You will have a great time. we just got off that one last month.
1. There are plenty of Tv's on board including your room. They have a couple of regular programming on there (all out of Colorado for some reason). My wife was able to catch Oprah and Dr. phil a couple times. Don't ask me why, lol. There is no CNN or Fox channels provided, but there may be in the sports bat in the front of the ship.
2. No laptop in the rooms, but right next to the above bar is the internet cafe ($$$$).
3. The Cayman's version of customs is a joke, they look at your sail and sign card and say "thanks". So, not tooo time consuming at all.
Cayman suggestion: Right after you exit the terminal and walk into town, to the left about 500-600 ft. there is this rasta guy selling cold coconuts that he cuts open for you right there with a straw. they were a tasty treat for like three bucks.
and there is no silly questions.