Okay, this does confirm that MySQL isn't running at all and this isn't a
case of missing socket file or misconfiguration.
It's just a file that tells the OS where to look for inter-process
communication. UNIX and Unix-like systems uses sockets, which are small
files that points to the memory address of the process for entry points.
Maybe I should change the my.conf and
No. Your MySQL server is looking in /tmp/mysql.sock so that's where it
expects it to be. If your configuration files already points to
/tmp/mysql.sock, then this is correct.
Apologies if I've missed this but did you already try running
mysqld_safe? Furthermore, did you do this as an administrator?
For example, I usually do this:
su admin -c 'sudo /usr/local/mysql/bin/mysqld_safe'
where 'admin' is my Administrator account's short name. Your
administrator account may be named differently, so change that
accordingly. You would then enter the administrator's password twice
(yes, twice). See if this succeed, then we can move further in fixing
the startup issues.