How can I prevent Always Allowed apps from counting towards App Limits
The text for "Always Allowed" says that it lets you use certain apps during Downtime or when the "All Apps and Categories" limit has passed. Unfortunately it doesn't say anything about not counting those apps towards any limits.

You could make a new limit that affects every app except Facetime, like this:



(Here I used the Camera app as an example, but you would uncheck Facetime instead.)

This does have the disadvantage that any new downloaded app under Social Networking would also not be limited, but you could monitor for that pretty easily.