1b. What's the best way to transport them (to keep them "clean")?
It depends on your luggage but I have two ways.
1) I have a camera bag with a mesh pocket on the underside of the top flap. When I keep dollars in this pocket (along with tickets and other important documents), no matter how much stuff I squish in the compartment above or below this tight, flat pocket, they're always still flat. Maybe you have an equivalent pocket somewhere in your luggage.
2) I fill ordinary business-size envelopes with cash & stash them throughout my backpack. I mostly only do this with kyat (even on my most recent trip, I was in areas without ATMs so I brought in all my kyat like in the old days) but I've done it with dollars as well. No matter the various lumps of clothes/shoes/whatever in my backpack, as long as I don't strongly crease the envelope itself it always seems fine. Keeps those 5000-kyat bills crispy as well :).