I have not specifically been on the Wonder, but I have been on the Magic and Dream. I may be able to answer some of the questions, but I can't answer any specific questions about Alaska and ports there itself.
1. Since temperatures are cooler there, you'll probably have to pack some warmer clothes as well. I would suggest looking at weather sites that give average temps, as well as the max and mins for the days that you will be there.
2. Technically, jeans are not allowed at dinner, but you will not be refused service if you don't. I've seen many cases where people wear shorts and tee shirts to dinner.
3. For the formal night, the tie with the nice shirt would be fine. When I was on the Magic in 2010, on the formal night, some were formal all the way to coat, tie, etc. On the other end, some were not dressed up formally at all. The only place where you would be required to be a bit more formal is at Palo, but that comes with an additional service charge.
4. I know they do the pirate night with fireworks, etc. on the Caribbean/Atlantic cruises. I'm not sure what theme they do for the Alaskan cruises.
5. I don't think it would be a culinary nightmare. When you are able to check in online, one of the forms is a dietary request form. You should fill that out and send it into DCL as soon as possible. They really do try to go out of their way for you.
6. The comedians/hynotists/entertainment is really kid friendly. They normally have a non-kid friendly show later in the evening in the adults-only area of the ship.
7. I did take a tour of the ship the first time I was on both the Magic and Wonder. If you have never been on the Wonder or Magic before, I would recommend doing it. It will help you get familiar with the layout of the ship, where things are, etc.
8. On the Magic and Dream, the spa areas and gym area are separate, so I would assume the same is the case on the Wonder. You may pass some of the spa area to get to the gym. There is no additional cost to use the gym.
9. Sea sickness medications are different for each person. What works for one person may not work for another. If you have been on smaller ships (fishing boats, etc.) and needed to use something for that, you may want to look into using the same thing. I have never gotten sea sick, but from others that have, said that even though they got sea sick on those smaller boats, they didn't get it on the cruise ship. I think that can be partly due to cruise ship having stabilizers that help keep you from feeling the rocking of the ship, unless in rougher seas. If you've never been on any type of vessel, I'd suggest going on a fishing boat or some other type of sightseeing boat at home before you go on the cruise so you can gauge your sea tolerance.
10. For port adventures, I'd suggest looking at the following link: http://disneycruise.disney.go.com/cr...re-excursions/ From this site, you can filter by port and look at each of the adventures available. They also include prices, so that should help. However, prices are subject to change.
11. In many cases, they will board people onto the ship once it is ready (leaving passengers off the ship and left the port terminal). Going out of Port Canaveral for the Magic and Dream, we were normally on board by about 11:30 am to 12 pm. The buffet is open once you board the ship. Staterooms will normally be available after 1:30 pm.
12. Since this is your first time, I'd agree to stick with the normal restaurant rotations. Even though you will rotate multiple times through the restaurants, the menu is different every night of the cruise. If something doesn't suit your fancy on the menu, ask your server for options. You'd be surprised at what they will do for you.
13. I'd refer you back to the answer in #10. Kayak rentals, etc. would fall under port adventures as well. Also, even if it isn't near the ship, they will generally take you to where you pick up and return the kayak, with transportation being provided back to the ship. Look at the port adventures link in #10 for more details.
From my experience, I suggest taking in all of the shows and entertainment on board. Many of them cannot be seen anywhere else.
If you have any questions, feel free to post or PM me.