if you create a gmail username in the U.S. and then say you moved somewhere in the U.K., when you log in and send out emails, will it display your address with @googlemail instead of @gmail?

And the next question is the same but in reverse: if you create an account in the U.K. and then move to the U.S. will your account now be @gmail or still @googlemail?

an existing @gmail address will also be in UK or Germany a @gmail.
the only thing that will change is the logo.
You won't see the gmail logo

All accounts receive e-mails send to both addresses – usernamegmail.com and usernamegooglemail.com