Yes.
Yes. Key will come from Toyota directly, my guess is from Japan, and the process takes a few days. In my case it was 3 days after I placed the order. Lipton guys can definitely help. Prices for shipping may very with shipping urgency and car model.
Yes. If you take your documents with you to verify.
Yes sir
Yes, I'm sure if you take your registration with you to their parts department they should be able to get you replacement keys.
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