Is the restraunt open and do you need a ticket to eat?

You do not need a museum ticket to eat at the Muse cafe. It is on the ground floor at the main entrance but located right before the paid section of the museum

There is a cafe on the main floor, but I seem to remember it being in the ticketed area.

Admission for museum.

It was a decent cafe; worth eating there. I also remember it being outside of the entry.