Yes
Yes you can
You need a membership to buy online.
Yes, you tell them you have never been in before and would like to see! It may be cash only on that visit, you could call and ask.
If you know someone who has a Costco membership card, and they are willing to take you with them, you can walk in the store with them on that day but otherwise, I don't know. You would have to call Costco and ask them. They just might do that. There would probably be a charge for the day.
Yes... membership is also required online
Yes I don't think you need a member ship if you order online
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