No Disney ships are US registry. They are Bahamas.
They have a medical center, just like all cruise lines. They can do a lot, but are limited too. Our last cruise last month a toddler was having seizures so they had a coast guard copter remove her from the hsip and take her to a hospital, Mostly they get people with infections, flu, sea sickness, fractures from falls, ear infections a lot from the kids,
I have never had to use them, but i have read several reports form people who had and they were all very impressed with their treatment and a nurse said she was very impressed by the amount of things they were equiped to take care of.
DCL does have a medical form on line that you can print out and get filled out by your doctor and then send it to the ship ahead of time so the doctor will be aware of any medical problems you or your family members may have. The wait staff will work with you on special diets too. But you must put that on the medical form and send it ahead of time.
The ship is pretty much wheel chair friendly.
Hope this helps a little,