To create a new database
Simply click on the Databases folder in your Folders section of the Navigation Pane. Then right-click and type your new database name into the Add box and press Enter. You then will be prompted to confirm the creation. 
You must have the necessary privileges on the MySQL server to successfully perform the creation, see your MySQL manual for more details and also have a look at Security Overview of MyCon, how you can setup these security privileges for different MySQL users.
To drop an existing database
Simply select the database you wish to drop in your Folders section of the Navigation Pane, right click and click on Delete. You will be prompted to confirm this step. If you accept you will loose all tables, structures, data, etc in MySQL in this database. However all MyCon files, ex. queries, scripts, reports, tasks etc will remain in tact (You will be prompted to confirm deletion of MyCon files associated with this database).