Problem with a cheater supervisor
I'm surprised that you have found any reasons to stay. I don't predict that you can have any happy future if you stay in this situation. There is clearly a lack of respect, maybe both ways. 

I can't think of any path to success whatever if you stay. Even if you can force better behavior, the resentment will come back to hurt you when you are ready to move on. I wouldn't expect any decent letters of recommendation. 

None of what you describe is proper. I hope it is uncommon. 

Find a better situation, even if you need to change universities. The head's lack of interest may make staying also impossible. 

Unfortunately, this advice comes with a heavy cost since moving will be difficult and you may not be able to take your research with you. The less developed it is, probably the easier it is to carry it away and continue. But you need a supportive advisor.