Can you bring in your own food, like a picnic lunch?

Yes you can bring in whatever you want, food, drinks, good luck charms. They do serve hot food there, you can order from your seat and they'll deliver it to you or you can go to the deli yourself.

I don't know about a picnic lunch though. Most places that offer food & beverage service would not allow that. Call and ask before you go to play.

I know you can bring food to the bingo area but that's the only place I know

Actually what I've done when I have a room for the night is bring snacks for the room an save money.