Try clearing the caches of Facebook, Facebook Messenger, Google Play Store, and Google Play Services.
Then open Google Play Store and try again.
If it still won't work, then clear the data from Google Play Store and Google Play Services.
Open the Play Store, and go through and reset your settings.
Wait for the security updates to complete, about 5 minutes or so, then try again.
If it still has problems, is there a possibility that you could have gotten an update from a different app store?
The app IDs are sometimes different from store to store, so one store may not be able to update an app from another store.