Allright. I have to correct me. Good that you pointed that out. I ment a cone, not a complete cylinder. Well, the cone was an example for a flashlight. I think for your projector is a pyramid ok. Just make sure to flip the triangles of the light beam.

MDL. Use the gradient filling tool in your photopaint programm. From white to black and then colored with color balance. Or just leave it white, black, grey...

Well the flash light effect is possible but you better try first to get the gradient beam. If that is too difficult for you, making a flashing screen will be impossible for you (it´s totally simple)... Doing a gradient texture is a joke.