Hanging misc inside, newbie questions

I'd be a little cautious using either command strips or the roll form of the same 2-side sticky foam tapes alone, at least for things that have a little weight to them like a shelf or something that gets stressed from being pulled on like a paper towel dispenser.  Bouncing down a Forest Service road is not exactly like the picture on your wall in your family room.  For me the combination of the compression of the screws on the tape and the adhesive with a tiny bit of cushion will keep things nice and snug without over-stressing the wallboard material or the vinyl wall paper coating on the walls.  And it's probably a bad idea to store an anvil on a shelf in a Pod, no matter how you attach the shelf.  Just saying.........

We mounted our paper towel holder on the underside of the cabinet over the sink using screws

For our towel rack in the head, I used coarse threaded short screws (<1") and 3M foam tape with sticky stuff on both sides.  It was the "extreme" mounting tape rated at 30 pounds.  The combination of the screws and tape is really strong.  I a bar for Ikea stainless steel rectangular bins the same way in the galley and they also have held very well.  I think the combination of the tape and the screws spreads the load a little between the tape and screws.

6 years ago we bought a cheapie mirror that simply hooks over the top of the door.  I believe it is 18" wide and 24" tall.  While traveling we take it off and lay on the bed.  At our destination we just simply hang it over the top of the door, works fine and no holes had to be drilled.  The mirror has 2 hooks on top, look like upside down U shaped brackets.

We put a full length mirror on the outside of the door to the head and it works fine.  There should be no reason why you couldn't put one on the inside.  Just use the little plastic mirror brackets that screw onto the door.  Hand tighten the screws so you don't over torque them since the door skin is pretty thin.  Just as with the door, you don't want to get it wet.