As far as I'm concerned, the need to use a real camera to capture real light is sufficient to thwart creation of truly convincing fakes.
Yes. It used to be the industry standard method for recording TV programmes prior to the invention of videotape recorders. If you know what you're doing and use the right equipment, the generational quality loss is very minor.
Back when everything was analog and low-resolution, had noise and artifacts anyway, sure. Do you have a video that compares modern digital 1080p with its best "Kinescoped" version? You have to deal with parallax, mismatched frame frequencies, pixels and differences between natural light and whatever spectrum the source monitor produces. I have never seen a recording of a screen that looked anywhere close in quality to the original in 1080p.
If it gets it to the point where it takes years of experience with this to figure out what is and isn't fake... I doubt that's any better than the situation without such a video verification system at all. In fact, I'd argue it's worse due to the fake seal of approval being given to the video.
As an informal comparison, check out a downloaded "cam version" of any recent movie compared with a DVD rip. If you ignore the occasional noise or interference from the crowd, the quality can be quite good.
Deepfake makes it less expensive to create fake video of someone, special signing cameras could make it expensive again in the face of that.