The Thai border crossing at Myawaddy/Mae Sot will open officially for overland crossings this month (probably next week or around mid-April after the Water Festival at the latest). This is the only overland crossing where travel to/from the rest of Myanmar will be permitted without permission. The Mae Sai/Tachileik crossing should allow overland crossings too BUT you have to fly to Tachileik or Kengtung from Taunggyi first as the road between Taunggyi and Kengtung has not yet opened (only the first couple of dozen of km from either side are OK to travel but not anywhere between the checkpoints, which leaves most of the road off-limits).
From China, the permit requirement for travelling between Mu-se (opposite Ruili) and Lashio has been removed since last month, however I'm not sure whether a permit is still required to cross the Chinese border overland in either direction via Ruili though. Please check with a Kunming or Ruili based travel agency and keep us updated. Forget about the Bangladesh border, it is definately closed and not safe on either side.
Just showing up to find a room should be possible, particularly in smaller towns where online booking is not an option. When it comes to Yangon, it's best to book ahead a couple of days as most accommodation is full most of the time there BUT if you happen to stumble upon a place, particularly on the outskirts of the city it's unlikely such a place would be full since most foreigners choose to stay in the city center.
ATMs are available in most larger towns and they definately work (VISA and Mastercard credit and debit cards accepted as well as Maestro etc.) the most reliable bank seems to be CB Bank but Kandawza is OK as well from what I've heard. The maximum withdrawal amount is 300,000 Kyat per transaction and there is a 5,000 Kyat user fee added onto that for each transaction you make.
Since Mar 31st, Yuan and Thai Baht can be exchanged at banks and money changers in addition to Euros, Singapore Dollars and of course US dollars. It is therefore no longer necessary to bring in only crisp US dollars. In February, I brought in some Euros and US Dollars, however, I exchanged everything for Kyat - I didn't spend a single US dollar anywhere.
I would therefore bring in any quantity of these 5 currencies that you may need and fund the rest of your stay using ATM withdrawals - and perhaps bring a small amount of US dollars just in case, but increasingly it is possible to avoid using US dollars whereas just a year ago this was not the case.
300 Yuan or $50 a day is a reasonable budget - in Yangon you might be pushing it a bit but hostels for $15-20 a day can still be found, otherwise most places go for at least $30-40+ and often much higher. In other towns, $30-40 gets you a good room, but $20 is the average for a cheap room.