Certain heads will only appear with certain models. Take the Spikey Wolf model for example; You can only have 3 or 4 (correct me if I'm wrong) suitable heads for that model. Some like the bear, the weasal, the rat, and the deer have only one head option. If you have Skinny, Fat or Original body selected you have more head options available. The same pricipal applies to tails.
Hope this helped
P.s: If you were missing body parts from the coding, your game wouldn't work at all.