They went back and forth on the Mongols. Remember that that the latter got as far west as Poland the Holy Roman Empire so it’s not like they hadn’t seen them up close. But they did romanticize the brutal Mongol derived warlord Timur or Tamerlane as something of an ally. Marlowe wrote plays about him.
Yes, and the back and forth presumably comes from rapidly changing local accounts and local perspectives, and the lack of a uniform strategic position on the Mongols across Christendom. They had that unity of purpose with the Crusades, but after their defeats, there was not a similar position vis-a-vis the Mongols.
The West loved Tamerlane until their leftist college professors changed his name to Timur.