Update:
I resolved the issue with the missing tables - my ISP required DB prefix + the length of the missing table names were too long for mySQL. Now the tables are created fine. Still can't run a scan, though.
I have: uninstalled Wordfence, Deleted it from the plugin folder, removed all of the wf tables from my DB, tried reinstalling every available version of Wordfence back to 3.6.7. Rinse and repeat.
No scan, no error in the php log files.
Ideas, anyone?