My insurance company is American National. They insure everything... golf carts, buggies, jewelry, general liability, everything... and have never once hesitated to pay out a claim... Almost didn't even ask questions. I think the only thing they DON'T insure, is special events, but you can just get a general liability policy for a year, and that will cover it, usually cheaper than buying special event insurance for one day... and you've got it for a year.
Yes, in California, they sell out of state registration stickers. Last time I checked it was $23, and was available pretty much everywhere. I'm not 100% sure it's required out there, but I would imagine so, otherwise there's no reason to sell them. Might be worth buying, just to make sure you don't get dicked with.
Bri, no plates, just a small sticker.