For a very good recent book on the subject I highly recommend The Gunpowder Age: China, Military Innovation, and the Rise of the West by Tonio Andrade. He sums up a lot of the information and theories available as far as china goes and concludes that the main cause does seem to be a relative lack of major wars.

Essentially, Chinese military technology underwent two different divergences compared to Europe. Prior to the mid 15th century Chinese gunpowder technology was on par with or better than that of the west. Chinese cannon was following European ones in the trend of longer barrels relative to bore size and the Ming army employed a larger proportion of handgunners than European armies would up until around 1500. By 1450 however the Ming had achieved a level of relative stability with no major opponents and military development stopped. Meanwhile in Europe over the next half century the "classic" cannon was developed and the matchlock arquebus started becoming widespread. As a result when the Portuguese first arrived in the 1520s both sides agreed that European guns and cannon were far superior.

This didn't last though, by the end of the 16th century and over the course of the 17th century warfare picked up again in china and European gun technologies were quickly adapted first by the Ming and later by the Qing as well. China developed complex drills and countermarch-style volley fire techniques even earlier than the Dutch did, and by the end of the 17th century they had defeated two Renaissance-style artillery forts. They even had plans to build their own but once the Qing had firmly established their dominance there was no longer any real need. Thus, Andrade argues, China had again reached a level of relative military parity with Europe. It was then over the course of the 18th century that again a lack of warfare combined with the relatively isolationist policies of the Qing dynasty led to a lack of military innovation and serious decline in the quality of the army leading up to a decisive defeat by the British during the Opium Wars.

/u/madmissileer

Check out several previous threads related to your post. 1, 2, 3.

Are any of my premises mistaken/oversimplified?

Yes, as the threads above explain, you need to look at not only "unit stats" but also the abilities of different entities in marshaling resources necessary to deploy them.

If it can be estimated, up to what time period could European firearms technology could be considered "equal" to that of other firearm wielding nations on other continents?

This is hotly debated. I think we simply do not yet know enough at this point in study. The thing is, development happened through a mix of evolutions and revolutions. The matchlock mechanism was such as revolution, attributed to Europeans. The recipe for gunpowder was another example, with the latest research attributing this to the Chinese. Corning is another major step, attributed to the Europeans. Thus, such a point of equillibrium may not exist.

Why did Europeans eventually develop superior firearms? Was it natural resources, technical know-how, more wars, doctrine, or some combination of this? And why was this effort not matched elsewhere?

If you look in the crucial period of 1450s-1600s, Europeans had a combination of: metallurgy, matchlock for handguns, improving gunpowder formulae, etc. Some are native developments, some are believed to have come from China (the how is still under debate). My advice is to not look at development linearly. Some other mechanism may have been invented in China or Japan, we will never know, and be combined with pre-existing knowledge in gunpowder and metallurgy.

For a nice overview, read Chase's Firearms.