Left side or back. I toss and turn so it may well be any position. Right though tends to bring some acid reflux or the like so I don't think I stay there for long. No idea what foam mattress but it's not too soft, typical sheet and comforter, single pillow. Nothing fancy.
When I was a kid I could sleep on the floor in a sleeping bag, not sure if I could pull that off now or not. I have to be pretty tired to fall asleep in a car (or sick), but as I get older power naps are starting to sound real good.