I had signed in for beta testing of many Android apps, but is there some way to tell which of the apps I am using is beta? Also, and specifically, how do I opt out of Facebook beta testing?
Mostly,you can easily get to know beta status of your installed apps by going to "My Apps" section in Play Store app.
See the article -
How do I stop using the beta version of Facebook for Android
Introducing the Facebook for Android Beta Testing Program
Regarding your first question, go into Settings->Apps, and click on each app in turn. The app's version number is shown just below the app name at the top and a beta version should be shown as such (the actual designation is unfortunately a matter for the developers, so there may be exceptions).
Can't help you with your Facebook question I'm afraid.