It sounds to me like you are living in an emotional pressure cooker and everyone in the family is reacting to it. Not knowing how to make things better, people have started to blame each other. The problem with that strategy is that even if it were possible to establish who is to blame in every situation, the root of the problem is still there.
You said that your parents are tired an irritable and that your father is moody and easily triggered into anger. It makes me wonder what kind of stress they are under. They may have been “protecting” you from their stress by not talking about it. But they may not understand that that kind of “protection” can backfire. Their stress is leaking out all over the place.
Rather than interpret their behavior as a lack of love, it might be more useful to ask them what’s going on. Be careful to not sound like you are accusing them. You will be more successful if you come at it with curiosity and a willingness to help. There may be nothing you can do about whatever it is, but at least you will know that their behavior isn’t really about you. It’s even possible that your parents are underestimating you and that there are ways you can help.
As for your sister’s boyfriend, of course you don’t like him. He sounds immature and insecure. For now, it seems that your sister is willing to accept his unacceptable behavior in order to keep the relationship. Like you, she is looking for love. I hope she finds someone more worthy of her. In the meantime, my best advice to you is to be polite but avoid him as much as possible.
I wish you well.