using singlesignon for mirrored site hosted by Dreamhost

I am maintaining our association's website hosted on a Dreamhost shared hosting environment. www.MYSITE.org. I want to set up a mobile-freindly interface accessed from the subdomain mobile.MYSITE.org, which is set as a mirror of the main site. I tweaked the .mobi module as per various suggestions in the archives and eventually got everything working EXCEPT logging in from mobile.MYSITE.org. If the user logs in from the main site (and therefore has the appropriate cookie), they can access everything thereafter through the mirror, but they cannot log in from the mirror. (Oddly enough, a new user can register through the mirror, even the registration confirmation directs them to the mirror, but even they cannot log in through the mirror.)

So: will the singlesignon module allow them to sign on to the site from the mirror?

If so, how do I set up the database? The documentation indicates that multiple databases are required, but currently both sites share the same database (mySQL). Do I need to set up separate databases? (I am unsure exactly what I need to do to create them, so detailed instructions would be welcome!)

If the database can be shared, is it still necessary to create individual folders under www.MYSITE.com/sites for each site with a custom settings.php for each site, or is the single default settings.php then sufficient?