While you wait for more targeted answers, here are some threads on how non-European powers progressed technologically in the Early Modern and Modern eras:

China and Japan

• What were some reasons that China turned inwards and neglected maritime exploration after Admiral Zheng He and his missions.
• This thread talks about the political situation in Ming China and how it contributed towards the dynasty's more inwards focus both before and after Zheng He's famous voyage.

The Americas

• Why is it that western Europe developed technologically so much faster than other places such as Africa/Native Americans etc. ?
• This delves a huge issue involving most everyone from the Americas to Australia to Asia. I'd recommend reading over the entire thread (even the downvoted comments) because this is a treasure trove of information and debate.
• The native americans and several other cultures did not experience the same technological advancements as europe. What has caused this diffrence?
• This thread starts with a huge overview done by /u/snickeringshadow which talks about the actual state of technology and development in the Pre-Columbian Americas which you might find interesting.
• What differences caused the Mesoamerican societies to be much more successful than Eastern North American societies?
• /u/Reedstilt delivers a huge amount of information on Pre-Columbian North America which may help illuminate the picture in which those societies lived.
• Why didn't native americans develop bronze, iron or steel?
• Lots of good information here about the use of metal in the Pre-Columbian Americas which you might find relevant (particularly due to metal weapons' utility in warfare).
• If there is iron in the Americas, why did mesoamerican peoples never develop iron working?
• The users in this thread delve into the difficulties of finding and smelting iron in comparison to finding abundant native copper and putting the relatively pure metal to good use.
• Is there any reason why the Native American civilization never was able to work metal?
• Here /u/Reedstilt this time draws explicit comparisons between the metalworking of Native American societies in the Eastern Woodlands and European metal working that you may find illuminating.

Africa

• Why were there so few empires in Africa?
• The answers in this thread correct the OP's assertion by pointing out various empires that developed (and collapsed) throughout Africa.
• What happened to Africa's Ancient Empires?
• The respondents go into the fates of several medieval and early modern African Empires as well as the difficulties of African history (often in finding evidence).
• Why did all of the other continents develop so much quicker than Africa?
• This is a large thread that not only talks about the African experience with "development" but also has several commenters highlighting the situations in the Americas and Australia. /u/khosikulu's comment here is an excellent analysis of African geography in context with its "development" and other issues that are commonly cited when comparing African peoples to others.