Facetime call history & Facebook message history
FaceTime calls do not show-up as 'FaceTime' on your phone bill.  It's simply a data transfer so it will be lumped-in with all other data transfers on your bill, you don't know what type of data it was, either.

FaceTime calls (audio and video) all go thru Apple's servers so they have a record of the calls.   Also, the iPhone stores the FaceTime history in a local database.  You can search this site for examples of software and techniques to get access to that database and look at it.  They all require you to jailbreak the iPhone so you'd need access to it for an extended period of time.

For Facebook, I believe you can search the history as long as it hasn't been deleted.  Here's an article on how to so that.  It's a few years old but I believe it's still technically correct.