This is your second question regarding "Why did ------ not colonise America" so I'll try and answer both of them.

Basically, it's a factor of ship capability, economy, and State interest. As for why not cross the Bering Strait? Well it would probably be because Alaska is not the best example of a place people would actively want to live, and the goods which come from Alaska (Lumber/Furs) are still abundant in China and closer Manchuria and Siberia. As the Second Edict of the Qianlong Emperor to King George III of England (1792) states: "Our Celestial Empire possesses all things in prolific abundance and lacks no product within it's borders. There is therefore no need to import the manufactures of outside barbarians in exchange for our own produce"

Along with this, there is more evidence that the Polynesians had themselves discovered parts of America, but less evidence of Chinese exploration. It's mostly just speculation for most Historians which entertain the idea.

That said, the Spanish Silver Boom is a good example why Chinese Economy and State interest shows why the Chinese Empire did not colonise America.

When Spain colonised and conquered South and Central America along with the Portugese, they acquired a glut of silver, which was the only good which China was willing to trade, so due to this, more silver was traded, and this upset the Chinese economy, most notably when the government began to require peasants to pay taxes in silver instead of a harvest percentage, which led to more cash crops and instability during times of famine. Eventually the Silver trade had negative effects of the Chinese economy, and over that period of time, while Chinese trade still existed, their Junkers become much smaller, and internal problems begin to damage the economy and change focus the State's interest on those internal instead of outer ambitions. Certainly, there was a point where China had the chance to be a naval power to rival western powers, but economic instability and different systems in society and government made it not so.

Why is the economy necessary? Well this explains why North Africa would have more difficulty in colonisation, but also explains the failure of the Scottish Colonisation of Central America. When the Scottish attempted to colonise Nova Scotia, and Panama, lack of proper naval supply logistics, and much more powerful opponents (the Spanish and the French) in the area forced them out. Colonisation expeditions were costly, and in the end, these became expensive endeavours which harmed the home economy more than it benefited, due to no return on the investments.