I had similar problem with my iPhone 6s. Aside from voice memo and video recording, normal phone call and FaceTime worked, but 3rd party app video & voice calls didn't. I plugged in my EarPods and it worked! I removed the pods and tried again, and it worked!
So I think the problem was the iPhone somehow thought that an external microphone was connected and therefore muted the built-in one. The static/crackles we experienced might be the iPhone trying to draw voice from unoccupied audio port. Me plugging in and then removing earphones might have triggered “microphone removed” event in the iOS and thus re-enabled the built-in microphone.
I hope this helps, if not you then someone else who are having similar problem.