Considering that the two China (mainland and Taïwan) were officially separated in the late 1940s/early 1950s and the history divergence between our world and the Fallout world started at the same period, there is a possibility that this separation never happened in the Fallout world to begin with...
Nope. Change in parallel universes is exponential- after divergence, the universe looks much like ours with an increasing amount of difference for every bit of time that passes. The events that caused the separation likely had roots before the divergence, so it likely occured in mostly the same way it did here. That, and the point of divergence is unknown, but the Fallout Wiki lists it as '1950s'.
In my fan fiction universe, the first noticable change was in 1947, the Roswell Incident, which was when the first threads of the shadow government (proto-Enclave) began to form. Later, the universe was totally unrecognizable: the Commonwealth Reorganization Act of 1964, the formation of the United States Central Enforcement Agency in place of SOCOM, etc.