I don't know about #3. Personally I'd want to check my bill before leaving the hotel to make sure there are no strange charges. Some hotels just slip a receipt under the door at night and let you leave your key in your room anyway for quick check out.
As for #5, you should. Or I should put it that the store should enforce it because if you don't you can contest the charge. The store would lose as they don't have your signature on file as it matches your credit card.
As for #4 and #6, YES, YES, YES! No one should do these things. Except at Costco as when you get a Costco card you sign an agreement stating that you give the store permission to check your receipt. Anyplace else, EVERYONE should refuse to give over personal info or their receipt as it's an invasion of privacy and there is nothing the store can do to you if you say no.