We have been on both the 4 night and 7 night Western. Sue's exactly right re the ship-- overall very acessble but elevators can be crowded plus they are on the small side, and the non-Disney shore stuff is not always ideal. For that matter, even touring on your own can be hard. For example, Cozumel had virtually no curb cuts and had a number of pillars blocking the narrow sidewalks. Also,
DCL does not have consistently reliable info about the accessibility of the shore excursions (which are not run by DCL). For example, we took the trolley tour in Key West, which SO was not a "very short walk" from the ship. I have seen people here have good luck renting a car to explore on their own.
Re special diets, I recommend putting your request in your reservation. Then on your first night, ask to speak with your dining caprtain and also tell your waitperson. They will work together to make sure that your needs are communicated to the chefs. You can also tell them where/when you plan to eat other meals so that you can be accommodated. Be aware that depending on your needs, you may need to eat breakfast/lunch in the sit down places (which are obviously more formal than some of the other options there) so they can custom prepare your meal.
However, the regular buffet style dining may also work well for you. We liked this the best as I could manage great (I have a soy allergy so some options like fresh fruit are obviously "safe") and it allowed greater flexibility. But this would depend on your diet. The breakfast buffets have typical breakfast stuff. Lunch buffets are themed (seafood, oriental, etc) and are different every day so can be harder to predict. Your dining staff can tell you what is on the menus and what the ingredients are. Also, the chefs are happy to come out and go thru ingredients for the buffet items. Everyone was very hepful.
Have fun! I hope this helped!

Cupcake