Yes, there is a charge for dining in one of the alternative restaurants, including Johnny Rockets.
This is the opening times for Windjammer onboard AOS:
Continental Breakfast: 6:30 a.m. - 7:30 a.m.
Full-Buffet Breakfast: 7:30 a.m. - 10:30 a.m.
Lunch: Noon - 2:00 p.m.
Afternoon Tea and Snacks: 4:00 p.m. - 5:00 p.m.
Dinner: 6:00 p.m. - 9:00 p.m.
Late-Night Snacks: 1 a.m. - 4 a.m.
Food limit? If you're thinking of the Windjammer, I don't think there's no limit at all =)