I was wondering whether it is possible to create a new database and user, from PHP, on an WHM/cPanel server.
As long as the user you use to connect to the database has the appropriate privileges defined in MySQL this shouldn't be a problem.
To create databases the user needs the CREATE privilege (to drop them that would be DROP privilege), to create user(s) you need to have the CREATE USER privilege. You also might need the GRANT OPTION privilege to be able to grant privileges to other users.
So as long as the DB user(s) you can create through WHM/cPanel have these privileges, you should be ok.