Ok - got it!!
Actually mysql and PHP were running fine after I changed the extension_dir to the correct directory.
The Problem after that was w/ phpMyAdmin and it's configuration.
Here's what I did to fix that:
'host' from localhost to the machine host name
'extension' to 'mysqli'
'user' to a user who has access to MySQL, i.e. can log onto MySQL on the server
'password' to the password of the user