What is the way to deal with a father who frequently insults and beats without cause, which has negatively affected my personality and made me consider leaving home, especially since there is a precedent with my younger brother who left the house?

It is well-known that a father's compassion for his children is usually dominant, and what you mention about your father is surprising. We advise you to supplicate for him so that Allah may mend his condition, and to be patient with his harshness, for patience is an act of worship and contains much good. You must honor him and treat him kindly no matter how badly he treats you, and beware of disobedience to parents. You should occupy your time with beneficial knowledge and righteous deeds to avoid friction with him, and there is no harm in leaving the house to avoid problems if there is a legitimate benefit in doing so. Seek the reasons for his ill-treatment and try to remove them. If the change was sudden, it might be due to possession or black magic, and its cure is through ruqyah (Islamic exorcism). Your brother must cease quarreling with his father because it is an act of disobedience, and he should be advised gently and kindly.