ما هي الحقوق والواجبات في المعاملات بين أبناء الأب وزوجة الأب، وهل يُعامل أهل زوجة الأب كأجانب شرعًا؟

Your father's wife is a mahram to you, and it is permissible to see her hair, neck, palms, and feet, provided there is no fear of fitna. Seclusion and shaking hands are also permissible under the same condition. You and your sister must treat her with politeness, righteousness, and kindness. As for the women of your father's wife's family, they are ajnabiyyat (non-mahram), unless there is a reason like fosterage or kinship, and they must be treated like other Muslims. The verse, "And he raised his parents upon the throne, and they bowed down to him in prostration," refers to his father and his father's wife, Leah, who was his maternal aunt by lineage and raised him after his mother's death.