If I arrive at Kashghar in early Oct and want to travel by road to Beijing and also see Great Wall. Wha to do?

It is around 4,500km between Kashi and Beijing, so far way. Are you sure that you wanna travel by road? It shall take much time! Though, here is my suggestion:
At Kashi International Bus Station, there are buses to Urumqi (almost sleepers). It takes around 22h. Then take a direct long-distance bus at Urumqi Nianzigou Bus Station to Yinchuan. Only one bus is aranged every other day and the duration is around 26h. After that, transfer to another bus to Beijing then, covering around 1,200km.

Except that, I suggest you fly to Beijing with a stopover in Urumqi.