1. How to resolve the error - can't connect to the local mysql server through socket '/var/lib/mysql/mysql.sock' (2)?

  To resolve the error - can't connect to local mysql server through socket '/var/lib/mysql/mysql.sock' (2) - 

Check the following First check if another instance is running in the same machine ps ax | grep mysql Then, check if your file my.cnf (probably in /etc/mysql/ folder) is correctly configured with

[mysqld]
datadir = /var/lib/mysql/
socket = /var/lib/mysql/mysql.sock

Next, you have changed the default data directory, did you gave the right permissions to the new directory now

 chown mysql:mysql -R /var/lib/mysql/*
 chmod 755 -R /var/lib/mysql/*

After changing the permission restart the service and check

service mysql restart