1. It looks like you'll have to create the database yourself, since SS can't automatically do it.
2. Does the installation die after the "I can't tell whether mod_rewrite is running." notice? I would assume that because it didn't detect mod_rewrite, it wasn't able to properly make, if at all, the .htaccess file for this installation of SilverStripe.
sharper - I've dug out an old Apache 2.0.55 / PHP 5.1.2 server, and Silverstripe v2.2.2 rc2 installs OK.
This is a long shot, but - do you have any functions disabled in your php.ini?
Check 'disable_functions' towards the top of the standard phpinfo() output - if "apache_get_modules" is listed, you could end up with the error you report
Alternatively: Does your host run PHP as cgi? If so, you won't have the apache2handler functions to return the available modules, so the installer tells the truth, if not the full story. Complete the install anyway, and check your .htaccess file - the rewrite rules should still get written and Silverstripe should be fine.