If you go to Eorpedia you will see the genetic makeup of the peoples of Europe. The R Haplogroup type originated in Arya (Afghanistan, Iran Uzbekistan, Krygistan, Tajikstan, Pakistan area around 20,000 years ago. They probably domesticated the goat and cattle thus the European facial features of prominents noses. The early Europeans who were hunter-gatherers probably had African or Asian features as they did have the calcium enriched diet from milk, curds and cheese. They were probably inbred as well. This kind of diet with high calcium content also helped bone growth so these people were taller as well. R1A Haplogroup type came into being either because of diet or mistake in DNA replication. They spread south into India, north then east and west. The southern group in India gave rise to R2 Haplogroup found nowhere else in large numbeers. The western group occupied Russia and the Black Sea area. Then R1B arose from the Arya region and spred westward towards Turkey and Balck sea area. The Hittites were probaly R1B Haplogroup Type. The R1A went from Russia towards northern Germany and Scandinavia overcomingthe inbred early Europeans. The R1B alongthe Danube entered Europe via Austria. They spread into central Germany into the British Isles as it was connected to the European mainland during the Ice age. These people overcame the early inbred Europeans. They are the Celtics. The Celtics in Anatolia went eastward into China and occupied the Taklamakan Desert in the Tarim Basin Xingiang or Sinkiang.
Central Asia during the Ice age was green and not desert-like as the glaciers were still there in the Arctic region and the Altai mountains. The Tarim Basin wasn't a desert at that time either. There was no concept of race as they were shephrds and followed thir sheep or goats. The race developed as result of their diet. Those who had low calcium diet had smaller noses.
The Central Asians were horsemen as the first domestication of horses occurred in Kazakhstan around 7,000 years ago or earlier from remnants of horse bones and so on from carbon testing. However, this indicates a system of horse stables and early domestification wouldn't have such a sophisticated system so domestication would have occurred earlier with a rudimentary system.
The similarity in name of Khazzar and Kazakhs leads me to think they were the same people. Genghis Khan changed the complexion of the population in Central Asia but there were gene exchange occurring all the time.
The Celtics in the Tarim Basin brought Buddhism into China. The region of Uzbekistan was known as Sogdiana in those days where traders from India , China and Russia met.