I understand that the Mongols viewed the Yuan as being "too Chinese" and may not have intervened on their behalf, but did the Ming understand that there had been a rift between the Mongol Empire and the Yuan?
How concerned were the Ming that the Mongols would try to repeat their successful invasion of China? What steps did the Ming take to prevent this from happening?
Why did the Mongols never attempt to retake China (or did they?)?
After the Ming retook China, the Yuan dynasty retreated to Mongolia and formed the Northern Yuan dynasty. Northern Yuan and Ming did fight on and off, and the need to defend the northern border from Mongol incursions prompted the Ming to rebuild the Great Wall (most sections of the Wall standing today were built in the Ming dynasty). That being said, the Mongols were not able to seriously threaten Ming control of China after their retreat to Mongolia because of civil war between various competing factions. The Ming intervened in these internecine conflicts in order to prevent any one leader from becoming too powerful.
The Turko-Mongol conqueror Timur did attempt to launch a full-scale invasion of China and allied with Northern Yuan to do so. However, he died en route and his empire disintegrated shortly after.