If your space for small appliances is going to be limited, I would say that an electric skillet with a domed lid plus a microwave will do just about anything you need to do. The skillet will do everything from pancakes to pot roast, which are a couple of things I can think of offhand that don't go well in the microwave. A crock pot would be good, too, but if I had to choose between the two, I'd go with the skillet. They're usually available for about $20 on sale or with coupons at department stores. The grill will be great, but you can't count on it because of weather. I assume that you will usually have running water available in a bathroom, so a kitchen sink size plastic tub might be helpful for cleanup, and a hand held shower sprayer might be helpful for filling it, depending on the layout of the room. I hope you will have access to your fridge because things would be much more challenging without it.
In hot weather think of serving lots of chef salads. It's an easy-to-fix meal if you get pre-washed greens, shredded cheese, pre-cooked or leftover meat. Good luck with your project!