They serve breakfast, lunch and dinner. I can't remember the exact times, but they're open maybe 7-ish in the morning til maybe 10 at night...with possibly some limited offerings later.
Yes, they have a large variety of breakfast foods. They are definitely open by 7 AM, though I think they start selling juice /cereal / fruit a little earlier
I think they still make beignets then... they also have giant cookies, homemade ice cream sandwiches (or you can just get the cookies or ice cream), I think they have cheesecake, pie... not sure what else