A) While it is true that the Uyghur people are Muslims, much of their faith and practices comes from folk Islam, which is much more mystical and superstitious. That is why the snake plays such an important role. It is believed that having a dead snake in the house will keep people from sinning (since sin entered the world through a snake). The dead snake shows victory over that and an ability to walk on God's road. You will often find them hidden somewhere by the front door of a home.
B) Kids at home are often forced fed cod liver oil or other natural products for health purposes, here it is snake oil that is said to keep children healthy.
C) This dried snake skin can be ground into a powder and put in a medicinal tea. The guy at the dry good store will use the same grinder for your snake skin as he does for your cinnamon sticks, so that everything can gain that nice reptile taste.