Was gunpowder adopted quickly, or did it take a while for the technology to start being used? What countries were the first ones to get this technology? At first, did the Europeans simply copy Mongolian and eastern designs, or were European innovations quickly implemented?
Any good reads or articles about this would be great, too!
The early history of gunpowder weaponry is a little murky. We can speculate that gunpowder was introduced to Europe through the Mongol invasion, and the seeming resemblance between early Chinese Firelances and European Handcannons does seem to bare this out, it is, in the end, just speculation.
I can't really speak to the development of Firearms and Artillery in Asia but I can say that once introduced into Europe the evolution of gunpowder weapons continued at a breakneck pace. The Handcannon first appears in Europe during the early 14th century and by the mid-late 15th had evolved into the Arquebus and was a solid enough weapon that the Black Army of Matthias Corvinus consisted of roughly 1/3 Arquebusiers.
The development of European Military technology from the High Middle Ages right through to our modern day is really, truly, astounding. Even before firearms were introduced into the mix the arms race between nations was going ahead full steam; in the context the development of arms, armor and metallurgy in the late Middle Ages and the Renaissance firearms don't seem nearly so alien as they may first appear and their rapid evolution part of a greater shift in gears.
I have no idea how to cite my sources but I got the ratio for the Black Army Here: G. Razso, 'The Mercenary Army of King Matthias Corvinus