What are the limits of interaction between a brother and his sister after the death of their parents? Is her obedience to him obligatory, like a father, or is advice sufficient? And is he permitted to strike her when enjoining good and forbidding evil?

The sister is not obligated to obey her brother in worldly matters. As for religious matters, he must enjoin upon her what is good and forbid her what is evil with wisdom, due to the general evidence for the obligation of enjoining good and forbidding evil. Changing with the hand does not necessarily mean striking; rather, it means destroying the instrument of evil or preventing the person from committing the evil act directly. Striking is permissible as a means to change evil to prevent its occurrence or continuation, while observing Islamic guidelines. However, after it has occurred, it is not permissible because striking after the act is for discipline, and the brother does not have the authority to discipline his sister.