Good post. I might point out though that insofar as Islam is concerned, had it not been for the resistance that the Mongols encountered with the Mamluks all of western Europe may have fallen to them.
Mongols did reach the dense forests of Germany, Italy, etc. But decided that there were not enough grass to feed horses. Thus, turned around. This was the only documented reason for not-occupying of western Europe.
Just something I used to have a big interest in.
Yes the Mamelukes were a big factor. I’ve also heard it argued that the forests and high numbers of castles made Europe less than appealing for the cavalry based Mongols.
A very large army could easily pass from Khanate territory directly into Eastern Europe without encountering any Mamluks. In fact, a Mongol general would have to rather go out of his way to come across them.
Different branches of the Mongol Empire were involved with the invasions of Europe and the Middle East. The Golden Horde were the ones who attacked Europe, while the Il-Khanids invaded the Middle East. In fact, the Golden Horde and Il-Khans eventually came to blows with each other.