How can one deal with a sister who has questions and objections regarding Islam, in light of the mother's severe opposition and verbal assault on Islam and her attempts to sever the relationship?

You must continue inviting your sister to Islam with wisdom, good counsel, and patience regarding your mother's harm. Do not despair or regret if your sister does not respond. Your answers regarding Allah taking the soul during sleep and the soundness of waking up, and concerning women's inheritance and their lack of responsibility for maintenance, are correct. Ask Allah for steadfastness and reward. Be gentle with your family and avoid provoking them or insulting their religion.