Currency situation

I was in Myanmar mid Oct - mid Nov. (1) yes. I had several US dollar bills rejected because they were creased. I thought they looked pretty good. Guesthouses or merchants would tell me that the banks require the unblemished bills, but I could never get a good answer on why the banks wanted such crisp bills. I brought mine from the States. I kept my bills crisp by cutting out bill size pieces of cardboard and placing the bills between the cardboard, held together with rubber bands. It worked great!
(2) I paid for bus tickets, food and lodging with Kyat. Often, you could get a slightly better rate with U.S. dollars than Kkyat due to their exchange rates. Many of the guesthouses clearly wanted $$. I took several flights within the Country and they always wanted dollars. I didn't take the train, except for the Circle Train (highly recommended). The Circle train in Yangon took Kyat.
(3) The larger cities or tourist areas, Yangon, Mandalay, Bagan, Inle Lake had reliable ATM's. I used them and I never had a problem. Personally, I'd bring some dollars. I don't like to rely on only one source of money, ie. ATM's.

I was in Myanmar from November 14 to the 30th and my experience echoes tomtraveller.

Even smaller denomination bills need to be in pristine condition. My hotel manager apologized but rejected a $20 bill I had saying it was the banks that were so picky..

I used ATM's in Yangon, Mandalay and Inle Lake with no problem.

1 - any $US you take needs to be in very good condition.
2 - everything can be paid for with Kyat now, so the only use of $US is to change into Kyat at official Xchange booths(can also change Euro and Singapore $, and $ Aust at a handful of changers)
3 - ATMs are very widely spread now...all the places a standard tourist will go, plus some. Local bank fee of 5,000 Kyat per withdrawal, and up to 300,000 Kyat per withdrawal. They work fine.

'Many of the guesthouses clearly wanted $$.' - I disagree....nowhere I stayed at last trip expected nor desired payment with $US...

My experience echoes that of rivaltribal. I spent 4 months in Myanmar earlier this year and never once used US$.
I made a few online flight purchases and a few hotel payments via credit card but all cash payments were in kyats including accommodation, entrance and zone fees for various sites and transport (bus and train). When prices were listed in US$ I simply asked for the equivalent price in local currency and there was never a problem. A few times the exchange rate used meant I paid a fraction more and a few times it even worked in my favour.
The government is actively attempting to strengthen the kyat and requiring it to be accepted for all purchases.

To clarify, I purchased a couple of flights through a travel agent or an airline office (I didn't book online). When I did this for a flight the next day, the agent wanted foreign currency (in my case U.S. dollars), not Kyat. If I would have tried to book online, it would have shown the flight as full. However, the savvy agents told me to return near the end of the day and there would be a likely spot for next day travel. I did this a couple of times and I always got the flight that I wanted. I prefer spontaneous travel so I prefer to book my flights just the next day. I didn't have an issue with this in mid November.

To clarify my statement about guesthouses preferring U.S. dollars ("Many of the guesthouses clearly wanted $$.') and rivaltribal's comment, "- I disagree....nowhere I stayed at last trip expected nor desired payment with $US..." it has to do with the price that they were charging for a room in U.S. dollars vs. the amount they wanted in Kyat for the same room. For example, for a $20 dollar room, they wanted 28000 Kyat (an exchange rate of 1400 Kyat per dollar). I was getting Kyat out of the ATM for 1275 per dollar thus saving around $2 per room. That's why I said many of the guesthouses clearly wanted dollars. It's not because they would only take dollars. They would take both dollars and Kyat but if you did the math, it was clearly better to pay in dollars, if you have them. Sure its only $2 but for 28 days, I'll save the $55. Yes, I will pinch pennies when I can. I noticed the same thing for many of the Conservation area passes around Began or Inle lake.

or.....you tell them you will pay in Kyat and at the appropriate exchange rate...
Also depends on the current Xchange rate - I actually saved some $$ by paying in Kyat at some places.

That's right. the bills should be in good condition, you can use both USD and Kayats, of course if you use locao currency it's much better. I saw ATMs in Yangon, not sure in other places.

ATMs - just some places - Yangon, Yangon airport, Mandalay, Mndly airport, Bagan, Nyaungshwe (Inle), Hsipaw, Lashio, Hpa'an, Mawlamyine, Myawaddy, Kengtung....etc. etc...they are quite wide spread.

1b. What's the best way to transport them (to keep them "clean")?

Make an 'envelope' from some card (e.g. old cereal packet). Put envelope in plastic bag (e.g. Ziploc)