We mostly use wormer with a Ivermectin base, but occasionally use another type to help hold down expenses and to insure they don't develop an immunity to the Ivermectin. That pretty much covers it, except for routine hoof trimming. We try to get them at least every 8 weeks, but some need it more often. The foals are usually very lightly trimmed at about 1 month of age and every month thereafter. Usually just a light touch with a rasp keeps them growing straight.
Donkeys can founder, contrary to popular belief.
Usually this will happen in the spring with the lush grass. Just introduce them slowly to a new pasture and it shouldn't be a problem. Start them at an hour the first day, two hours the next day, etc. It's easiest to determine the condition of your donkey by running your hand across the ribs. Middle of the road is best, and sometimes its easier to feel it than see it if they have a heavy coat.