Can I prevent Facebook from running in the background? I made the observation, that turning off Background App Refresh does NOT prevent Facebook and FB Messenger from receiving updates and giving me notifications and thus still run in the background. This awesome answer shed some light on the matter explaining that there are a quite a bunch of means for apps to run in the background unaffected by the Background App Refresh setting.

However, I want to ask this question point blank: Is it not possible for the user to completely kill an app, meaning no background activity whatsoever, other than removing it from my device?

This is not about battery life or something, but about Facebook (or some other service) being able to track my (approximate) location based on my IP address.
In the iOS device:
you can go to settings > general > Background App Refresh and try to disable Facebook

In Facebook:
to disable Location in Facebook settings > account Settings > location > location chose Never

hope with does 2 options I can give you the answer you want