You do not need to install the classifieds in a separate database. The classifieds is prefixed with a separate prefix so same database is fine.
To fix your issue you need to do one of two things.
1. Run the install script again and answer all the forum stuff correctly.
2. Go database diving in the cp_settings table and change setting with id of 83 and 182 which should be the database and cookie prefix settings in that table.