1. I don't know the prices, but some hotels that are decent from what i know are: Bay Hotel, A&EM, Asian Ruby, Silverland. You can check out the prices online.
2. Yes you can pay everything by VND no problem, 250SGD seems like a lot but it really depend on what hotel you staying since it is the bulk of the cost. Ofc also depends on what is ur makan and drinks budget. Why not you book hotel and pay online? Seems like the better option rather than carrying more cash. In that case then you just need around 50SGD/day IMO. More if you are splurging. I'll advise budgeting 50SGD/day and bring more SGD just in case.
3. Rates are pretty bad now. Even for online transfer services where the rates are near FX are like 1:16,700 now. Usual rates can be like 16,900-17,100. Not sure where to change in Singapore but in HCM usually people go near Ben Thanh gold shops or the currency exchange I shared before: