I would like to fly NokAir from Bangkok to Yangon. Do they ask for proof of return flight? I know AirAsia doesn't, but for example, Thai Smile does.

I avoid NokAir like the plague. It is a certainty that if you look at the departure board at DM, there will be a least one of their flights cancelled. I'm told they pay peanuts so always have a pilot shortage. I flew them at one time from Khon Kaen, but twice in a row there was a delay of nearly two hours (for a one hour flight) before a turbo-prop rolled up to the gate. No thanks. I fly anyone but these days.

I think it depends on Myanmar policy. 

Depends on your Myanmar visa. A Business visa on arrival doesn't require a return flight, valid for 70 days but does require a letter of invitation from a Myanmar company......checked thoroughly before departure from Bangkok.. Local nationals from SEA countries get a few days no questions asked.No idea about a tourist visa.

Check online...all the info is there.