Using a database class in my user class

Question

In my project I have a database class that I use to handle all the MySQL stuff. It connects to a database, runs queries, catches errors and closes the connection.

Now I

Answer 1

As he said, put all your functions in the database class and use the database object to access those functions from your user class. This should be the best method in your case. Eg:
global $database;
userclassvar = $database->doSomething();