How to fix it qulickly? ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

I know that there are many of these questions here but I didn’t find the answer for my problem.

So I have a production server running a few websites with a few databases. I had some performance issues so I’ve edited the mysqld.cnf file, then tried to restart Mysql but it gave me an error:

Job for mysql.service failed because the control process exited with error code. See "systemctl status mysql.service" and "journalctl -xe" for details.

Can’t see any specific details there. So I’ve tried to run: mysql and I got this error message:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

I’ve now replaced all the default settings before changing my mysqld.cnf but I still get the same error.

I’ve also checked if any mysql servies are running but there’s none. And the /var/run/mysqld/ folder is empty. I’ve tried creating some empty files there with the corresponding names, but no luck.

What is the issue here and how can I safely restore it? My sites are currently offline…

mysqld.cnf:

    #
    # The MySQL database server configuration file.
    #
    # You can copy this to one of:
    # - "/etc/mysql/my.cnf" to set global options,
    # - "~/.my.cnf" to set user-specific options.
    # 
    # One can use all long options that the program supports.
    # Run program with --help to get a list of available options and with
    # --print-defaults to see which it would actually understand and use.
    #
    # For explanations see
    # http://dev.mysql.com/doc/mysql/en/server-system-variables.html
    
    # This will be passed to all mysql clients
    # It has been reported that passwords should be enclosed with ticks/quotes
    # escpecially if they contain "#" chars...
    # Remember to edit /etc/mysql/debian.cnf when changing the socket location.
    
    # Here is entries for some specific programs
    # The following values assume you have at least 32M ram
    [client]
    socket=/var/run/mysqld/mysqld.sock
    
    [mysqld_safe]
    socket		= /var/run/mysqld/mysqld.sock
    nice		= 0
    
    [mysqld]
    #
    # * Basic Settings
    #
    user		= mysql
    pid-file	= /var/run/mysqld/mysqld.pid
    socket		= /var/run/mysqld/mysqld.sock
    port		= 3306
    basedir		= /usr
    datadir		= /var/lib/mysql
    tmpdir		= /tmp
    lc-messages-dir	= /usr/share/mysql
    skip-external-locking
    #
    # Instead of skip-networking the default is now to listen only on
    # localhost which is more compatible and is not less secure.
    bind-address		= localhost
    #
    # * Fine Tuning
    #
    key_buffer_size		= 16M
    max_allowed_packet	= 16M
    thread_stack		= 192K
    thread_cache_size       = 8
    # This replaces the startup script and checks MyISAM tables if needed
    # the first time they are touched
    myisam-recover-options  = BACKUP
    #max_connections        = 100
    #table_cache            = 64
    #thread_concurrency     = 10
    #
    # * Query Cache Configuration
    #
    #query_cache_limit	= 1M
    #query_cache_size        = 16M
    query_cache_type = 1
    query_cache_limit = 256K
    query_cache_min_res_unit = 2k
    query_cache_size = 80M
    
    #
    # * Logging and Replication
    #
    # Both location gets rotated by the cronjob.
    # Be aware that this log type is a performance killer.
    # As of 5.1 you can enable the log at runtime!
    #general_log_file        = /var/log/mysql/mysql.log
    #general_log             = 1
    #
    # Error log - should be very few entries.
    #
    log_error = /var/log/mysql/error.log
    #
    # Here you can see queries with especially long duration
    log_slow_queries	= /var/log/mysql/mysql-slow.log
    #long_query_time = 2
    #log-queries-not-using-indexes
    #
    # The following can be used as easy to replay backup logs or for replication.
    # note: if you are setting up a replication slave, see README.Debian about
    #       other settings you may need to change.
    #server-id		= 1
    #log_bin			= /var/log/mysql/mysql-bin.log
    expire_logs_days	= 10
    max_binlog_size   = 100M
    #binlog_do_db		= include_database_name
    #binlog_ignore_db	= include_database_name
    #
    # * InnoDB
    #
    # InnoDB is enabled by default with a 10MB datafile in /var/lib/mysql/.
    # Read the manual for more InnoDB related options. There are many!
    #
    # * Security Features
    #
    # Read the manual, too, if you want chroot!
    # chroot = /var/lib/mysql/
    #
    # For generating SSL certificates I recommend the OpenSSL GUI "tinyca".
    #
    # ssl-ca=/etc/mysql/cacert.pem
    # ssl-cert=/etc/mysql/server-cert.pem
    # ssl-key=/etc/mysql/server-key.pem
    innodb_buffer_pool_size = 4G # (adjust value here, 50%-70% of total RAM)
    innodb_log_file_size = 128M

Error message

    ● mysql.service - MySQL Community Server
       Loaded: loaded (/lib/systemd/system/mysql.service; enabled; vendor preset: enabled)
       Active: activating (start-post) (Result: exit-code) since Wed 2017-11-15 15:41:40 CET; 20s ago
      Process: 15879 ExecStart=/usr/sbin/mysqld (code=exited, status=1/FAILURE)
      Process: 15871 ExecStartPre=/usr/share/mysql/mysql-systemd-start pre (code=exited, status=0/SUCCESS)
     Main PID: 15879 (code=exited, status=1/FAILURE);         : 15880 (mysql-systemd-s)
        Tasks: 2
       Memory: 344.0K
          CPU: 305ms
       CGroup: /system.slice/mysql.service
               └─control
                 ├─15880 /bin/bash /usr/share/mysql/mysql-systemd-start post
                 └─15933 sleep 1