How do you screw stuff into the walls?

If you use expanding screws, keep in mind that once they're there, they are there for ever.  You can't remove them without really damaging the wall.  Using coarse thread screws leaves a small hole that's easy to fill.  If you use the 3M 2-side sticky tape, you risk pulling off the vinyl wall paper, but with care, a razor and some solvent, you can usually get it off without hurting anything.  You have to cut the tape through the foam part between the two sticky sides very carefully, then the solvent will weaken the glue bond enough to take it off without hurting the vinyl.  Be sure to use a solvent that doesn't dissolve the vinyl, as would acetone, for example.

Yeah, I'd lean toward molly bolts for insulated walls because they'd likely provide enough force to expand into the foam. The trick is finding ones short enough. The shortest I can get locally is 1-1/4"; the shortest one in StephenH's link (22mm) would probably work.

+1 to lostagain. That fastener is meant to drill through drywall so you can cut off the tip and predrill through the plywood. Keep the total length to 1 inch or less so you don't hit the outer wall. Longer wouldn't make it stronger anyway since the fastener threads are only engaging with the thin plywood, screwing deeper into the foam does nothing. Start with a small pilot hole so if by some miracle you happen to hit one of the few aluminum square tubes that constitute the rpod wall frame you can use a self tapping screw into that. Wrap a piece of tape 3/4 inch from the drill tip so you don't accidentally drill through the outer wall.

For interior walls, I use these:

Lots of good info given. Makes me feel better about mounting something light to the walls.

Thanks