Is there a long-distance bus from Nalati Town to Kuitun City?

No, only go to Yining City first and take the train

Not in the town, but there is a ride out of the town. Kuitun Station

It seems that passenger vehicles are not allowed on the Duku Highway, so if you want to go directly to Kuitun on the Duku Highway, you can only take a small car. If you stop by public transportation, you need to detour to Yining and walk several times longer. (for reference)