My view,
You can carry both US $ and kyats. But it's illegal to accept US$ from tourist. Once you arrive to YGN airport, there is a Foreign exchange counter (open by government) Tourist must change minimum 300$ or something like that with US$ equivalent special note called FEC. You can sell them back once you reach your hotel reception. You no need to go around and ask people for the money changer as there is none. It's illegal to buy dollar from tourist but you can change every where. But remember you have to pay hotel charges with US$ or FEC.
You no need to carry around your passport as you need to give at the hotel.
There are some black area for foreigners. Like you go Aung San Suu Kyi house
. But not alot.
You can change back to dollar when you go back. Just easily ask the reception counter (price may be abit different but it's not much)
Like "pearl" say, it's very safe in Myanmar. Much much better than malaysia.
Good luck bro