Yes a mirror site uses the same db.
You can manually create tge database instead of letting the installer do it for you.
The one click installer does create a random db prefix to make your sites harder to hack. Just edit wp-config if you import other tables that don’t have the random prefix.
In short, almost everything you’ve asked can be changed with an edit to wp-config.
To change the db password you have to change the actual db password from the dreamhost panel, but you will also need to edit the password in wp-config to match what you set in the panel.