Hello,
1. You can give "mysql" command on the shell and if it shows following output (mysql prompt) then Mysql is working fine.
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root@test [~]# mysql
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 317435 to server version: 4.1.21-standard
Type 'help;' or '\h' for help. Type '\c' to clear the buffer.
mysql>
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2. You can restart MySql using following commands :
# service MySQL Server restart
# /scripts/restartsrv mysql
Even you can add MySQL Server from "WHM >> Service Configuration >> Service Manager" which will monitor MySQL Server service and automatically restart it if it goes down.
Let us know if you need any further assistance. We will be glad to assist you.
Best Regards,
eUKShane 
http://www.eukhost.com