Is it normal for a father to be like this?

That's abuse.

No couple can be together long enough to have a teenage child and not have had a lot of disagreements and dealt with a lot of tensions along the way. No parent is always thrilled by everything their child does.

But of course how you describe your father treating your mother - and sometimes you - is not reasonable or caring or kind.

Nobody here can know what's going on in your father's head or what label a relationship counsellor or a psychiatrist would apply to him and the relationship between him and your mother. In fact, while you obviously see and hear a lot of what goes on between them, even you can't really understand the dynamics of their relationship, and you can't know their total history or even everything that's going on in their lives at the moment.

It's not your place to try to heal their marriage, and it's not for you to try to get to the bottom of why your father behaves as he does and help him be a better husband, father and person. When it comes down to it, he has to recognise that he has a problem, and he has to sort himself out.

As for your mother, I can only assume that she's getting _something_ out of the marriage, even if it's only a roof over the head of her and her daughter, and food on your plates. It's not unusual for women (and sometimes men) to find themselves locked in dysfunctional, damaging relationships and unable to see any way out. Sometimes practical factors mean that's true. Sometimes it's not true, but rather due to a lack of self-worth and self-confidence. Sometimes that low self-esteem is the result of stuff that happened way back in the person's personal history, and sometimes it's due to living with a highly manipulative person who has steadily chipped away at it for many years.

I'm sure it's very difficult to watch what goes on between your parents, and I wouldn't be surprised if you feel like you're walking on eggshells when your father is around, but I assume you have no option but to live with your parents right now. It seems to me that the best thing you could do right now is start thinking about how you can get out of the family home, even if that's a long-term goal. I really don't think you should talk to your father about his behaviour, since, at best, he'd just dismiss it as the chattering of an ignorant, naïve kid, and at worst, he could react very badly with serious consequences for you and your mother.

I wouldn't be surprised if you find it difficult to respect your mother for putting up with your father's crap, but do your best to try to understand things from her point of view. People always do the best they can in whatever situation they find themselves in, but sometimes they just aren't equipped to handle them very well.

He should join the military.

He had low self esteem and takes it out on your mom and you. My dad was the same. I left home at 18 and joined the air force just to get away.

If he says rude stuff like you're a worthless piece of shit that's not normal. It is normal for parents to get mad at their kid or significant other, but to an extant. You should talk to him about how you feel about how he is treating you and your mother. hopefully he is gonna understand but he could get mad. There is no human on the earth that can always be right. Even the smartest person on this planet makes mistakes. The best thing to do is to own up to it, if you don't you will feel guilty even if it's years from when you did it.