Re: China discovers N. America
Mary Anne talked about this here, and other space enthusiasts have noted the parallels with a nation that turned its back on exploration. I have not seen the book, or any other evidence that they landed in the Americas, but given what I know about Chinese history, their early explorations, the Zheng He fleet in the early 1400s, and their eventual isolationism, I would not be at all surprised to find it true.
Certainly if China had developed an expansionist philosophy, there would be one hell of a lot more people speaking Chinese than there are now.