PJs are generally designed for use low-down when not inverted, so you would probably have trouble getting the image down from the ceiling! , unless your Ae700 has a tricky way of getting around this...
Somebody else would have to confirm that though, I've never seen one myself.
Sure - the AE700 projects straight forward and you've got the same amount of vertical shift up and down, so if you want it on a shelf near the ceiling then that shouldn't present any problems.
I can't see it being a problem. The panasonic remote allows you to do anything you might conceivably do with the control panel on the projector. The infra-red eye to receive signals wouldn't be affected by putting it on a shelf and the lamp indicator's not something you need to see anyway - either the thing's on (and you'll hear / see it) or it isn't.