I appreciate how hard you tried to be fair and to take responsibility for your part in these arguments. Yes, you need to be respectful. Yes, you need to work on learning ways to control your anger. And yes, you need to learn when the best thing to do is to back down and walk away. You know your dad has anger management issues. You know talking back will only get you hurt. So why would you do things to provoke him? You won’t win any argument with him so please quit trying.
The answer to your question is that it doesn’t matter how common or uncommon it is for parents to beat their children. It isn’t right for any parent to be violent and to beat his child – no matter how much the kid provokes. My guess is that your mother is as afraid of your dad as you are. If she intervened strongly, he might turn on her. Her only way to protect you is to try to mediate. I do suggest you try to talk to her when you can be calm and rational about it and when you can sympathize with the tough spot she’s in. Perhaps if you work together, you can come up with some better ways to handle it when your dad gets upset.
You do have some other choices as well: You can know in your heart that violence is wrong is wrong and keep clear of your dad by staying out of arguments. (It doesn’t matter how “right” you are if you end up getting hurt.) You (and your mom) could seek out help from a domestic violence program. Check out this website/a> for information. Or you could notify the police the next time he beats you. I do strongly suggest you try out the first two options before resorting to the third. Once the legal system gets involved, you lose control over what happens next. The police have protocols they have to follow. Do call the police if all else fails and you are getting hurt, of course. But try getting connected with a program to end family violence first.
I’m very sorry you don’t feel safe with your dad. It’s certainly not the relationship I would wish for you or you would wish for yourself.
I wish you well.