I took my two sons ages 3 and 1 1/2 at the time on the Paradise 2 years ago. They have a nice selection of normal children's menu itemes in the dining room. Spaghetti and meatballs, mac and cheese, pb&j, hamburgers, hotdogs, chicken fingers, etc. My kids loved it. My 3 yo was fine sitting in the dining room. My youngest I did have to take little walks, but was ok too.
As for leaving them in the program for dinner, generally no. On formal nights they do have a children's dinner, so IF your child will stay, he can have dinner with the other kids and you can eat alone. He may want to eat with you though.
Ours stayed one formal night, and ate with us the other. We got so many compliments on how adorable they were all dressed up. You'll have fun, but do expect it to be a family vacation, and expect to be together most of the time. That way if he wants to be with you instead of in the program, you won't be disappointed, and there are a lot of nice things to do as a family. The kiddie pool is a lot of fun, but does become a wave pool with the ship's motion at times. Bring water and sand toys.