You made your point dating to the shang, and I dont disagree.

Well, as i read about the history of China, previous entity of Xia apparently didn't conquered anyone and even if they did, we don't know, written history of China start from the late Shang period.

About the rest Tankiedesantski answered you about the "republican ideas" of ROC, i can only add that even if you deflect yet again to "real Legitimacy lay with the people" there is nothing more really legitimate by the people than popular revolution which led to the state being supported by 90% of population.