Water and food outside or you'll regret it. They dont need it over night anyway. As for size, I would just google how many sq ft they need and go from there. I have a 10x10 A frame coop that both chickens and ducks go in. Its prenty big enough for my adult 7 ducks and 14 chickens with room for more.
Ducks don't need food at night, and can be weaned off of water at night as well, but if it isn't a big deal then I would recommend having water available for them at all times. We don't coop our waterfowl but rather keep them in 20' x 20' pens with a 8' diameter stock tank buried in the ground. Some sleep on the water and some sleep next to the stock tank. We keep a large sized water bowl with fresh drinking water in it at meal times.