Yes
As long as you are a member, yes. If you are not a member and you received the item as a gift, you will need to become a member or go with the original member that bought it.
Yes they can look it up if you paid with a debit or credit card by the credit card or debit card or look it up by your membership number
You probably can. You go to the membership desk and they can look up the item. So as long as the item came from Sam's Club, you should be ok.
Yes, if you paid it with a card (debit or credit) and have it with you
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