Not wrong, but not necessarily right either. It would be a question for those with detailed knowledge in the matter, which is neither you nor I. Does having a strong naval tradition push the adoption of gunpowder among one's army? Or at least would it make the Chinese gun technology be on the same level as the Europeans, who had been fighting gun wars among themselves for a good while now? Especially as China would have been unified for a while now?
Depends. As a counterexample, see the Ming efforts to subdue Vietnam.
Key word being Vietnam, which is close, rather than the Americas, which are far far away. Naval explorations would likely follow the relatively unpopulated west coast, which isn't very profitable without masses to work it, before China could even get to the populated Central America. If China hasn't subdued its own neighbors closer to it (Japan I think, the Philippines I'm pretty sure of), somewhere so far off will be a much lower priority.
Cuba and Florida; doesn't seem quite as nice as silver mines, especially since the sugar industry wans't set up in Cuba until the 17th century.
Who's saying Cuba and Florida? I was talking about Central America (maybe closer towards Panama), and then there's always South America as well. Besides, so what if China landed on the Pacific Coast first? Its only yours if you can hold it, and if Spain comes with troops while China can't hold it, suddenly it belongs to Spain.
Mmm. The story about the year plays a part, but a bigger part was strange foreigners with the weapons of the god who were able to play the diplomatic game with finesse, and the Chinese could get an interpretter, and presumably smallpox would ravage the empire like it did in OTL.
Don't forget La Malinche (who knew both languages fluently from the start of the Aztec invasion) as well, who played a very heavy roll in that "finesse" (Cortez himself wasn't exactly subtle or kind). Even should China find its own interpreter, China isn't guaranteed a diplomatic coup either. China
could make the mistake of picking the wrong side in an attempt to be subtle rather than outright conquest, in which case China is in a much worse position.
About smallpox, though, I don't know (how strong/comunicable was smallpox in China?). On one hand, it could do as you say. On another, might different Chinese practices cause a different effect? You'll have massive die offs sooner or later, but if its later rather than sooner...
Of course, smallpox ravaged ironworking Chinese vassals is still quite different from what the Spanish met.