Ann, if you are Chinese, then I think that most people in this region would automatically assume that you were from one of the ex-Soviet Central Asian republics, where people look more or less Chinese too. There are some people from those countries who have settled in the European CIS countries. I saw some, both in Ukraine and here in Belarus. Not a lot, but a few families and individuals - all speaking native Russian.
You don't need to show your passport a lot anyway.
If you were to travel alone, just do what I do: Keep a low profile, smile and be friendly (but not in an OTT way - just low-key). If you are struggling to communicate, apologise for speaking poor Russian - people are tolerant towards that.
People here are very friendly towards strangers, must be the culture thing (?)
As for the US political question: Most people in the CIS area are very up-to speed on politics - and a bit cynical about it. They are more intellectual than Western Europeans in general, and much more so than Americans. I think they are smart enough to see you as an individual, not an representative of US foreign policy.
Belarus DOES offer visas to Americans - I saw some info about it at the Belarus consular section at their embassy in London. There can't be a lot of Americans visiting Belarus as tourists though. But there might be Americans visiting for NGO type work or other projects. Also - the "bride" market is still in full swing.
But I think you can count on that people will NOT expect that you are a Chinese American. At first, they might wonder why you don't speak Russian.