What is the legal status of my mother, and is she considered divorced, given that my father uttered phrases of divorce such as: "I will divorce you, you are unlawful to me, I have divorced you, why are you here," along with frequent disputes and expelling her from the home?

Divorce does not occur merely by the father saying: "I will divorce you" or "You are forbidden to me" (unless with the intention in the second phrase). However, his statement: "I divorced you, why are you here?" could be an explicit divorce or a declaration of what he intended by the prohibitive صيغة (formulation), and his intention should be sought to clarify this. The father should be advised to fear Allah and beware of taking the words of divorce lightly, and to treat his wife kindly, in accordance with the Almighty's saying: "And live with them in kindness." Children must honor their parents regardless of their actions.