can you leave the museum and then come back later during the day ?

I was able to when I talked to the person who scans the ticket to come back in from the food exit. Make sure they know about how long you will be out and if they will still be the one sitting there. I was able to leave for therapy in my car and re-enter an hour later. Very accommodating with open communication.

Yes, just ask the ticket taker for a hand stamp.

Yes

Yes. They will give you a hand stamp.

They will as a matter of fact. Ensure you inform the attendant. Excellent museum with courteous staff!

Excellent museum!! from another level