I can't think of a better vessel or itinerary for your first cruise. It's one of my all-time favorites.
Here's another set of answers to your questions.
1. Princess seems to begin the boarding process around noon.
2. I suspect that you can buy the motion sickness bands or patches at most drug stores, but don't waste your money on them because sea sickness won't be a problem for anybody on this cruise. At 77,000 tons, MV Sea Princess is big enough so that you won't notice any motion, especially on calm Caribbean waters.
3. I have stayed in the cabins located amidships on the Aloha deck on a sister ship and didn't hear a thing, even when spite of "sleeping in" on mornings at sea when the pool area was the center of activity. The cabins do seem to be insulated very well.
First 4. You can order off the dining room menus for room service during meal hours -- but why do you want to do that? The staff in the dining rooms are most wonderful!
Second 4. Absolutely! Some people will tell you that it's the best port of call on the "Western Caribbean" itinerary. Princess Cays has one of the most magnificent that beaches you will find anywhere (white sand), and there are also reefs for snorkeling and plenty of "toys" (banana boats, wave runners, paddle boats, etc.) if you wish to rent them. Before the passengers go ashore, the ship's staff brings in about four tons of food and beverages, opens the bar, and fires up the barbecue pits for one of the nicest barbecues that you will find anywhere (yes, it's included in your cruise fare). There's also a band playing island music, a volleyball court on the beach, a couple gift shops where you can bill local, a supervised play area ("Pelicans' Perch") for young children, and some hammocks in a shady grove if you want to stay out of the sun. I'm ready to go back!
Since you are going on the Western Caribbean itinerary, be sure to stop by your local sporting goods shop and get a pair of Surfwalkers, or similar footgear, before you go because you will need them to climb the Dunn's River Falls in Ocho Rios. The stairstep falls are easy to climb (one woman climbed them at 99 years old!), well shaded, and very refreshing. If you have never been to Jamaica before, I recommend the tour that combines Prospect Plantation and the Dunn's River Falls with a 1/2 hour shopping stop. The plantations in Jamaica's Blue Ridge are really fascinating, as they extend from sea level up to the tops of the mountains. At 6300 feet, the Blue Ridge is considerably higher than Mount Washington. There's quite a science to the way in which they plant various crops at various altitudes to yield an impressive array of produce. The Jamaican Blue Mountain coffee is a great souvenir. (Yes, it's legal to bring the roasted beans, either whole or ground, back to the United States.)
Grand Cayman is undoubtely the best island for serious shopping on the Western Caribbean itinerary, and it also offers some wonderful attractions. The "Sea and See" tour, which includes a visit to the wrecks of the SS Callie and SS Balboa in a "semisubmersible craft" (actually a boat that does not submerge at all, aboard which you sit below the water line and look out through windows in the hull), during which you also will see lots of coral reefs and marine life) with a land tour to the rock formation called Hell (looks volcanic, but actually is limestone eroded to razor sharpness by algae), the sea turtle farm, and a photo stop at seven mile beach. Many passengers also rave about the excursion to Stingray City, where you actually get to swim with and pet live stingrays. If you are "into" the beaches, Seven Mile Beach (which really is only 5 1/2 miles long) is one of the best in the world, and the island also offers plenty of opportunity for snorkeling and scuba diving. The duty-free shops in George Town stock true quality merchandise of every imaginable kind, and the rum cakes (http://www.rumcakes.com
) also make great souvenirs.
Finally, Cozumel offers a dilemma. The most extensive Mayan ruins are on the Yucatan Peninsula at nearby Tulum, but that's a rather long trip involving a ride across the channel to Playa del Carmen followed by a 90-minute bus ride to get there and the reverse on the return trip. It's worthwhile, but be sure to bring a liter of water with you if you go (you can buy it before leaving the ship) and to drink it progressively to prevent dehydration. Alternatively, there's another tour that combines an outstanding Mexican folkloric show in San Miguel de Cozumel with a tour of the Mayan ruins at San Gervasio, which is on the island of Cozumel. The ruins at San Gervasio are much less extensive than those on the mainland, although they probably are much more profound because the island of Cozumel is holy to the Mayans. Of course, you also could dodge this dilemma completely by opting for either a day at the beach or a "New Waves" expedition for snorkeling or scuba diving.
Do have a great cruise!