GPG Key
 

How do GPG Keys work? Is the key attached to the RPM file? Is it possible to change the GPG key to match something else?

I tried answering that in a few sentences but kept adding things and blowing out the size of my answer.

I'd suggest looking through the docs at http://www.gnupg.org/(en)/documentation/index.html and asking any specific questions you might have. At least that way you'll get all of the information...

Is a GPG key part of the file - like even if the file is moved/copied does the key stay with it?

You're talking about 2 things at once there. You sign a file with your private key and transport the signature file with the file (they are separate). The private key stays with you and other people can use your public key to verify the signature.

Have a look at the gnupg site. You can download files as well as signatures for those files. There are other ways to do this - signing/encrypting attachments for emails, etc. That's why it's worth looking through the docs.