Scrolling rainbow when projector screen is in frame
You are seeing the scan line of the projector.  You need a camera with a screen sync feature in order to deal with the rolling shutter issue and depending on the technique used by the projector, it may not even be possible.  

What you are actually seeing is what the projector actually does, it's just that it happens too fast for your eye to perceive it normally.  A video camera is however fast enough to catch it.

This is regularly a problem even for professional gear and it is not at all uncommon for video screens to be shot with the device off and the video on the screen composited in after the fact.