Yes, at first they reportedly even wanted to literally murder all settled people they conquered (those were northern China mostly) to make place for more pastures but got convinced by rich tribute to just sit back and enjoy the racket. Their counquest of China was long and bloody (took 3 generations from Genghis to Kublai) and the Yuan dynasty was probably the most hated and reviled in history of China - that mostly went on the head of Kublai though, Genghis is seen more positively, mostly because respecting the Mongols for whom he is the foremost national hero.

It’s difficult to answer. Ghengis’ empire was brutal but which empire wasn’t? It would’ve been class-based in a similar way as Europe at the same time, where the ruling class also an elite military body and usually related to each other. So even if it wasn’t as bad as other empires, it would’ve still been bad.

The difficulty is that most of what is ‘common sense’ knowledge about Ghengis (a) focuses on the conquest, rather than what happened afterwards, and (b) is written by westerners who cannot be trusted to write about Asians. We need a book about the era (not just during Ghengis’ reign) like the one about Rome by Parenti.

A lot of dynasties did that.