yes, if you do not create a folder for the install, the on-click will put it in one for you
Create a new database right there in the one-click installer. Name it anything you want.
Your host name will be the a subdomain: yermysql.yourdomain.com
Since databases are on shared servers, you need to make your host and database names unique. Don't use a database you've already set up, unless it's empty.
Once you get a one-click script at your domain, you will receive an email with instructions on completing the installation (nothing is ever really "one-click"