Being somewhat new, I suspect few have done this. But what happens when one gets a new passport? Is it easy to transfer the Elite Visa Stamp or whatever they give you to the new passport?

I suspect you would have to use both passport until the visa expires.

I don't think they would be able to do a new visa sticker. I suggest you contact Thai elite about it.

Probably not at local immigration. You may have to connect with Thai Elite rep at one of the supported airports....or Bangkok. Let us know what they say.