ggarza,
The camera is some thirty feet of wire, both forward and below the level of the audio board. If I had that wired, I could run a line level signal up to the camera and inject it at that point. The camera should be made so that its audio and video are in sync, so that would improve things by one part, still leaving whatever delays are introduced by the switcher(s) and the DA. And does any delay get introduced by Facebook? I don't know. I doubt it, but the Facebook video is lower resolution than the camera output, so there's a layer of video processing there.