You’re dealing with a hell of an experienced IT Crowd type girl if she can grab a still of your face and use it to find your Facebook! But if you insist on doing C2C with the CIA then go ahead!
C2C is fine if done through AW system, they won’t be able to find any details and even if they could an IP address doesn’t link to one person, it barely links to a location and can easily be forged, changed, misled or other.
Your main concern should be them recording the session and then threatening to release it. A simple upload to a pornhub type site and you’re on the internet for anyone, friend or foe, to find.