I am looking for a true German word for a Computer user with "extra permissions and education". Any suggestions?
Both expressions are common expressions in German, but at least for me the have different meanings:
A key user is a special trained user. The user is not part if the IT-team, but a user and (s)he is a connection between users and IT-team. See also Wikipedia.
A power user is an experienced user who knows the program very good and uses much more features as the standard user (these guys makes the life of key users difficult, because the ask question the key user can't answer and must be forwarded to the IT-team). There is a big chance, that power users become the next generation key user.
In my business key users are called key users (it is an undertsandable foreign word). Key users also teach the normal users and in this function they are also called Multiplikatoren (ok, also no pure German word, but the origin is not English).
The official Microsoft language portal for translation their products says, that the right translation for Power user is Hauptbenutzer (main user in free translation)
You can search the IT terms on your own here.
For someone who works in IT, you could say Systemadministrator or Nutzer mit erweiterten Rechten (in contrast to a user with a guest account or with standard permissions).
For someone who likes to tinker with computers at home and has some knowledge, being it related to hardware or software, you could take a look at the answers to this question.