You can only define a single background image for a screen, so in order to have 4 different background images for the same screen, you'll actually have to create a screen, and then make 3 copies of it, and assign to each one a different background image. But there's no way to randomize the screen selection. You'd have to make the first screen for round 1, the second for round 2, etc.
Assuming you've created 4 copies of the same screen, each with a different background image, you could then create 4 Screen Sets, each containing only one of the 4 screens. Then set the conditions for the first Screen Set to (using "Advanced Conditions"):
level % 4 = 0Set the conditions of the 2nd Screen Set to:
level % 4 = 1Set the conditions of the 3rd Screen Set to:
level % 4 = 2Set the conditions of the 4th Screen Set to:
level % 4 = 3Also, I can't seem to figure out how to have my global properties override all backgrounds other cells may have set up. Any idea what I may need to do for that? If anything, that is the most basic problem. I can live without the first thing being possible.
I'm not really sure I know what you're asking for this one. On the Screen Properties (press the Properties button in the Screen Controls section), there are options to "Override all background colors (make them transparent)" and "Override all borders (turn them off)". Is this what you're looking for?
FYI, you didn't mention what version of the software. The above is valid for version 3.