Is it true that the bus number 936 goes directly to Mutianyu? No change in Huairou.

No, you need to take public bus no.916 Express or 916 to Huairou North Avenue (Huairou Beidajie) Station first. Then transfer to bus line h23, h24, h35, or h36 to Mutianyu Roundabout. Afterwards, walk about 500 yards (450 meters) to the ticket office of the scenic area. Hope helpful!