There were several warrior queens and princesses in mongolian armies, and they even had leaders. Khutulun is often referenced as one of the fiercest female women in human history. Mongols definitely had women in their armies, especially as horsemanship and archery were taught to both genders, and that was the biggest factor of mongolian shock tactics.
http://badassoftheweek.com/index.cgi?id=822456431891
Did they massacre the Khwarezmid Empire and remove their entire existence from history? Yeah. They are are where we get the expression "Don't shoot the messenger." Genghis had sent in a caravan to open up trade with this kingdom saying they wanted to have them join his empire. Had he only refused, they might still have survived as slave or in some other degree of history. Instead, they were mercilessly massacred to every last soul. Why? They murdered that entire caravan in challenge of Genghis Khan. I'm not gonna say that massacring people is a nice foreign policy, but they were kicking sand in the face of a dragon.
As for the bubonic plague, I get the idea that it would have been inevitable that it spread to the west eventually with terrible results. I don't get the idea that they intentionally were trying to spread plague though. The mongol's were immune to it, as many people in the asiatic world were, since they had grown up around its sources and developed immunities. Plague warfare isn't really one of Genghis Khan's usual tactics, but psychological warfare is. I believe the primary reason for throwing bodies was to demoralize enemies who were stuck in the castle the were attacking. Causing one of the worst plague epidemics was kind of just a side effect. It would have happened anyway as the east and west started to mingle more throughout history.
I feel like you can't ignore things like Pax Mongolica or the reinforcement of the silk road, the distribution of technologies, or religious freedom that mongolians brought. They even would accept local cultures and aspects of religion, and let people govern themselves, which pretty much meant for the most part if you said you allied with them, they would leave you alone. It wouldn't really affect your life much. Genghis also banned things like torture. They did execute people rather gruesomely, but they didn't torture.
I just think the Khans in fallout, despite being "based" on Mongolian wartribes, don't really take advantage of how cool mongols were, and I just feel I would have liked a more mongolian based antithesis to face the NCR than what we got in the Legion.