There's no way to transfer an account to a different region. If you want to login your wow accounts Europe at US version, the only way is editing your realmlist.wtf file. Because that link describes connect your wow game client to other servers.
However, it doesn't change what type of account you have or where your characters are stored. The only reason you'd want to do that is if you had both an EU account and a US account, and wanted to switch between them without installing a second copy of wow. And if you have only an account, you will need to buy another accountswow (wow accounts EU or wow accounts US) on a safety web like farmer100.
If you used the authentication key, it can not be used again since they are only valid once. You would have to give away the CDs themselves without any issues. It doesn't violate the EULA here in NA, so I don't think it should in the EU region.
How to play EU wow account and US wow account both in just one version? I can give you a way to solve the problem. Here’s what you should do:
First, you have to get two accounts, or sign up for two accounts if you don't have two accounts at both two versions.
Second, Open your World of Warcraft folder and look for ‘realmlist.wtf’, please open it up in a text editor
Third, You’ll see a option "set realmlist eu.logon.worldofwarcraft.com". Change the ‘eu’ or ‘us’ to the one you want to login in you will run.
If you’re on different game servers on the EU and US version, you’ll be initially presented with the new character roll screen. Choose the same server settings that you did originally and hit ‘Suggest Realm’. The resulting pop-up screen will suggest your originally chosen realm, just click ok and you will own your existing character list load up.
You can switch back though the same step above but change back the ‘eu’ or ‘us’ and you’re sorted. There are many EU and US wow accounts provided on farmer100, maybe you can buy another account to experience different version in a short time.