Q: How to create new MySQL database
A: Go to CPanel, then locate "MySQL Databases" panel.
1) create new Database (enter text like db or web)
2) create new USERname (enter text user name and password)
3) give rights for this (select Database User Name) over (select Database Name from drop-down menu), check give all rights.

Q: How to delete old database
A: Go to CPanel, then locate "MySQL Databases" panel and click on it. Now you will see a list of current mysql databases on the table from the left, and in the middle all db users associated with it. To delete click on the X on the right.