Sure they did. Why do you think Sichuan is now Han? It didn't used to be.
China expanded its borders PLENTY. It just had a lot of land nearby to do it in. For a significantly smaller cost than shipping people en masse across the Pacific.
China expanded its borders, but it seems to (like Russia) have just incorporated its colonization into the state. There were no areas that were developed as something like New England, say.
This isn't a bad thing, I suppose
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But its not as if the options for outside China (as in the modern borders, + Taiwan) are "across the Pacific" or "nowhere".
Culturally China may have changed (queues come to mind as the first thought), but it seems to have been - by the point of the late 15th century - slowing down on the innovations that drove economic and/or military power.As for the static culture--Chinese culture changed plenty. However, much like the Papacy in Europe it was usually very skilled at incorporating these changes into a traditional framework. Things were the same as they'd always been in China for a long, long time, despite being quite different.