Considerations for hanging a short throw projector and RSG Pro

The ViewSonic short-throw PS502W will typically be 6 or 7 feet from the screen.   My recommendation is to turn on the projector, hold it in your hands, and then move it around until you see the projected image fill your screen.  Make sure the lens is fully zoomed out.  That is the best technique to determine the distance.  You will use the Vertical Keystone feature on the projector to account for the angle when mounted in the ceiling and projecting at a downward angle to the screen.

There is no interference between the LED strobing from the Launch Monitor and the projected image from the projector.

It's a low risk with your setup, but theoretically, if the exhaust of the projector is blowing on the Launch Monitor, then it will shorten the life of the electronics.  Heat is bad.  The Launch Monitor is designed with heat sinks to dissipate the heat through the metal exterior under normal conditions.  Direct hot exhaust will interfere with this design.  You would need to have it within 12" with direct exhaust for it to be a problem.  Note that some projectors have exhaust vents that go off to the side and would not blow directly on the Launch Monitor.

A simple trig calculation is a reasonable estimate.  Keep in mind the ball at the tee location will be in front of the launch monitor by about 32".  Typically, that means the ball in the tee area will be about 10' from the screen.  If the projector is 6' from the screen, then it will only be about 4' in front of the ball. 

Assuming you are mounting the projector on a 10' ceiling, with about 10" down to the lower part of the projector after accounting for the projector mount.  You would need a 66-degree vertical launch to hit the projector.  If you move the projector further back or the tee location further forward, then the vertical launch angle will be higher (less likely for a ball strike).