Not true at all. China has lots of local dialects and nuance, but is over 90% Han ethnically and believes strongly in "one China," and has for literally millennia.
I also believe that if China did not have a powerful central government it would break into several republics, starting with Xinjiang and Tibet.
But the interesting part of this is that the central authority not only works to stop secession movements, but also to make sure minorities have a place in modern China. In general they try to favor minorities getting into college, by lowering the grades (from the overkill high school test) a minority student needs to enter college. That and general promotion of a minority's culture in primary school (like dances, language, etc) tend to ease the friction that both the Han have towards some minorities and the minorities have towards the Han Chinese.
its arguable either way. imo China is less ethnically diverse but more culturally diverse. eg. a large portion of the country speaks in a language unintelligible to the rest.
regional differences are more pronounced in China. I'd be hard pressed to figure out where I am if dropped into a random city in the US, compared to China
USA is successful because of other reasons.