When I select recent post from the menu bar, I see some old topics that no longer exist. If I click on one of the nonexistent ones, I get a 505 page error. How do I clear out topics that no longer exist from my recent posts?
You have done some manipulation from the database which makes these issues, Go to Dashboard > Forums > Dashboard And press Clean Up Button, After delete all caches and press CTRL +F5 twice in your browser page.
Also, if you have cache plugin exclude wpForo from the cache plugin, check the link below for more info about cache:
Please navigate to Dashboard > Forums > Moderation admin page and check the topics. How many Approved and Unapproved topics you see there? Do you have any unapproved topics?