My daughter is 6 and she ate with the kids in the Oceaneers club a few times. The previous posters are all correct.
For lunch, they usually go to Animators Palate which is closed to everyone but them. It is not buffet, they get served a specific dish. This was usually between 11:30 and 12:15.
For dinner, they go to topsiders, usually from 5:30 to 6:15. Topsiders is closed to all other guests (not that they would stop you if you wished to go, but it is only the kids food). The children in the Oceaneers club did not serve themselves (at least not that I saw). They were given a tray that was loaded with some of everything. I wasn't there the whole time, but I do believe if they want more of something, they can get it or a counselor will assist them.
As for the bathroom question, if someone goes to the bathroom, the counselors go out with them.
Hope this answers your questions...