I wouldn't characterize China as progressing slowly, but rather, stagnating badly. I mean, they were still using crossbows against the British in the 19th century. Once the Chinese closed their borders in the 15th century, they pretty much stopped any innovation.
Japan suffers largely the same fate during the Edo period. They go from a vibrant, changing society in the 15th and early 16th century into a heavily codified, stratified society that doesn't really change for three hundred years until the Meiji Reformation, and even then, it isn't until the end of the Second World War that they really begin to change.
India, as well, has had access to firearms nearly as long as the Europeans, yet doesn't see the rapid changes that affect Europe. I'd almost say, in my rather uneducated, gut reaction, armchair historian opinion, that Europe is something of the outlier for rapid change.
Generally speaking, I think you are getting this backwards. Sure, in some ways Europe certainly changed more rapidly than major eastern powers, but citing this as being due to eastern stagnation is flawed. It is not that Europe changed more rapidly than eastern powers, it is more that Europe stagnated and declined greatly after the fall of the Roman Empire, and it had delayed access to the major innovations that it had to import from the east much later. For most of the European medieval era, it was centuries behind the Middle East, China, and India in terms of technological, cultural, agricultural, and industrial advancements. Europe changed radically in later centuries because it was playing catch-up by importing generally completed technologies.
To address more specific things you have mentioned...
India never stagnated. At the time it was divided up by colonial powers, it was a fully modern society with a fully modern army. The main reason it fell to colonial powers was because it suffered a major period of political instability just as the European nations were gaining power due to the colonization of the New World (which they benefited from mostly due to physical proximity). Even then it took centuries of conflict for Britain to eventually take control.
Japan's Edo period was an odd case. It was mostly isolated, certainly, but it still underwent major cultural and societal changes during that period. All the values and culture of modern Japan emerged in that period, and it was due to the societal changes of that era (including the growth of a powerful merchant middle class) that allowed Japan to rapidly industrialize and become a major power as soon as its borders opened after the Meiji Reformation. It was far from stagnant and unchanging.
As for China... It was the center of the world and progress for most of human history. In many ways, it stagnated simply because it outpaced the development of the rest of human civilization. It was so much more advanced, developed, and wealthy than any other region of the world that it simply didn't need to trade. No one else had anything it didn't already have. And it was so large, well established, and populous that significant cultural change was extremely difficult to implement. And this was basically true for centuries and centuries. It was surprisingly close to being a modern industrial society in the 12th century. As I think my brother may have mentioned earlier in the thread, it may well be considered a fluke of geography that the steam engine was invented in 18th century Britain rather than 12th century China.
As for why things fell apart for China in later centuries... That is a very, very complicated issue. Simply saying that they stagnated because they closed their borders (which itself isn't even at all accurate) is a very, very flawed perspective. In truth, no one can really say why it happened. The best trained and most well-studied historians in the world can't really agree or understand on the hows and whys of it happening, so trying to apply armchair history to it is pointless.
I suppose it is fair to say that China is a great example why gunpowder doesn't at all lead to some kind of rapid forced societal change. Of course, it was amazingly modern from the point where it actually developed gunpowder and gunpowder weaponry, starting off already centralized and not at all feudal (the last Chinese feudal period was in pre-Christian times).