I think all these problems are due to the fact that you run an OpenVZ system...
Starting MySQL database server: mysqld...failed.
Please take a look at the syslog.
[b]/usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (12)'[b]
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
What's in the logs? What's the output of
ls -la /var/run/mysqld