You have the option to change your site's "home" directory in Domains -> Manage Domains.
Then click Edit for your domain and change the Web Directory to /home/username/domain.com/subdirectory
A redirect is a kludge since your main content is in a subdirectory, but can be done. Do a forum search here for "redirect," and I'm sure you'll find much information.
I don't quite understand what you mean by "move the database up 1 dir." If the database contains paths, then you can manually update the database via phpMyAdmin, located via http at the database server you specified.