How can I get back to paid PD 11 after having installed PD 12 and failed registration?

Hi HeiniS, the Parallels End User License Agreement permits one copy of the software to be activated by a single license key on a single computer.
If you have multiple license keys for the software, you may activate that number of copies of the software on the same corresponding number of computers as you have license keys( This rule is applicable for all the version of Parallels Desktop).

If you would like to use your Parallels Desktop for Mac license on a new Mac, you should sign out of the account the license is registered under on the Mac you don't need anymore.
Click on the Parallels Desktop menu, and select Account & License. In the activation window, click on your account email address and select Sign Out.
If you try to use the license on a new Mac without signing out of the old one, then upon activation on the new Mac you will see a warning that the license is already in use.
If you click on Activate on This Mac, the current copy will be successfully activated, and the license will automatically be deactivated on the old Mac.