Simply adding,
1) 뒤 is possible. '너 뒤에 뭐 묻었다' --- 'You got something on your back'.
2) 허리 is rather smaller part than human back. It's from the top of the buttocks to somewhere near the mid-lower part of the rib cage. 허리=waist. But, usually when someone says '허리 아파요', the pain usually refers to backpain, the lower part of the back.
3) 등 is commonly used to refer to 'back'. '등 좀 긁어줘.' ---'Scratch my back, please.'
4) I don't understand.. 차 뒤쪽에 means the back side of the car..