You've hit on one of my pet peeves! The same naming of decks on totally different ships! We also loved our balcony on Grand Princess, but they're not the same on every ship, so I can't answer your first question.
We loved Anytime Dining. We always asked to sit with others and were seated immediately. If you want a table for two, you may have to wait, but not any longer than a land based restaurant. They'll give you a pager and you can go have a drink (or whatever!) and you'll be paged when your table is ready.
IMO, it's definitely worth going ashore at Grand Cayman. Even if you don't have a tour planned there's lots of shopping and bars and restaurants. Just "people watching" is fun. The "thing" to do is one of the Swim With the Sting Rays tours.
On our last cruise we did the Island & Stingray Tour which takes you to the Turtle Farm, the Rum Cake store, Hell, and the Stingrays. We had a great time! This was on NCL, but I think Princess has something similar. Check here:
Have a wonderful cruise!