Technically, there is no food court, but there is a counter service, fast food place called Gasparilla's Grille.
Yes, they do offer refillable mugs.
Not all the restaurants are going to be available to you without a PS. For example, the character breakfast and character dinner at 1900 Park Faire typically do fill up. Citrico's and Narcoossee's are only open for dinner and again, they can get crowded during peak dinner times. The GF Cafe is open for breakfast, lunch and dinner. As with most resort restauraunts, I think they do keep some seatings available for their on-site guests, but if you are looking to seat a large group or dine during peak hours, I would strongly suggest making a PS now or as soon as you arrive at the resort.
All the buildings are very nice and you won't end up with any parking lot views. You can request a marina view in Sago Cay and that's considered garden. If you want to be closer to the pools, then Boca Chica or Big Pine Key are good choices. Conch Key is set back a little bit further, which makes for a nice quiet area. The walk between the 2 furthest points, is probably no more than 2 or 3 minutes.