The issue had nothing to do with the machine being a vps or whatever. It had to do with lack of debian admin skills, as you said.
You can specify repositories (collections of packages that can be installed) in the /etc/apt/sources.list file
as well as in any file inside the /etc/apt/sources.list.d/ directory. Thus, your original repositories were specified in a file inside this directory, and all you had to do is edit it, adding " non-free" to the end of every repository line.
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ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)
See you are not getting an authentication error, but a connection one. Mysql server was simply down, so you should have tried to start it first "/etc/init.d/mysql start" and look for errors in the mysql log if it didn't start.
We're sorry to see you go, good luck with plesk!