I'm not particularly fond of the food they serve there. Your best bet would be to go to a diner or restaurant on Hempstead Turnpike or go to the food court at the nearby Mall.
Yes, you can bring in your own food. One end of the Red Planet Cafe has tables for people who bring their own.
No. They have a cafeteria on site. They stopped me from exiting the cafeteria area with a coffee. Most museums don't let you walk around with food. If you have dietary issues I'd eat before or after.
You can bring food in to the Cafe area. You just have to consume food and drink in the Cafe area. Food and drink are not allowed in any of the galleries.
Thanks! Your answer is awaiting moderation.