Is there a cafe or somewhere to eat?

Yes, there is a small cafe area inside the museum. There are other cafe's and restaurants in the neighborhood around the museum.

Yes, there is - they sell the basic snack stuff, like hot dogs, pop corn, pre-packaged ice cream, etc. There is a cafeteria as well that sells more things, like basic salads and sandwiches. Last time I went, I packed my own food.

Yes. You think they call it Foodworks.

Yes, by where you purchase tickets. However you may get lucky and there are street vendors outside somethings. That's the way to go

Yes—right by the entrance if Im not mistaken

Yes

Yes and it's pretty good