1. In Cpanel, go to Mysql.
Enter the name for the new database in the New database box and click on Create database.
Enter a name in the Username box under Current Users.
Enter a password for it.
Click on Create user.
Now you need to add the user to the database by selecting each in the drop-down lists below that.
Click on Add User to Database.
Below that under Access Hosts, add either that person's IP address or % for anyone in the Host box.
Click on Add Host.

They can now use remote software such as Mysql Admin, Mysql Control Center, etc to connect to the database only. There are several free remote clients available for this.

2. You can see the contents of a database in phpmyadmin. There is a link to it at the bottom of Mysql in Cpanel. You may see one database there which the server has created for testing itself.

1. The port is 3306. Be sure to enter the FULL database and username exactly as you see them in Cpanel. The full names include your cpanel username added to the name you entered.

2. Are you saying you don't see the phpmyadmin link at the bottom under Mysql? Is this a Linux account or a Windows account? You cannot tell if a database is linked to any script in Cpanel.

No way to tell what a database is used for other than going through its content in phpmyadmin and then checking any urls or paths it provides.