Can you ask for a free popcorn bucket so you can share with your friend?

No but they have folding cardboard boxes to carry your snacks in. They easily store a medium popcorn. I've seen moms buy a large popcorn then dump it all in a few boxes for the kids before going back for their free refill.

They will most likely give you one of the cup holder trays

I've never asked but I don't see why not

I don't think so.

Yes

I think they will give you complementary cups