Are you able to connect to the database other wise? (through phpmyadmin f.ex)
Have you installed any new plugins or modified any core files?
No I'm not able to connect to it in any other way.. It just happend when I was reading a thread.
Then the mysql server on your host is down, try contacting them.
Could I enable it again myself?
And even more important: is there any way I could get the data of mysql on my pc without accessing phpmyadmin? (With any command in the shell or something)
And is it also possible to use a mysql database on another database? If so, please explain it in detail.
If the mysql server is down you can't do anything with it if your not the servers administrator.
Connecting to MySQL database with shell
MySQL database on another database? Another database structure? Like MsSQL?
MySQL database on another server I meant.
Well you can. In inc/config.php just change the hostname setting to your new server's IP address or hostname.
Be aware though if you decide to use a MySQL server not within the local network of your web server, you may notice a significance speed decrease as the web server and MySQL server must "talk" over the internet.
I entered an IP adress in the config.php but it still gave me the same error... could you give me an example config with an ip etc?