Is a woman's request for divorce—due to her inability to live with her husband, along with offering him compensation—considered Khulʿ, and is she obligated to return the dowry or household furniture to him to absolve herself?

A woman is not permitted to seek a divorce unless there is a valid reason, such as disliking her husband and fearing she might not fulfill his rights. In such a case, there is no blame upon her for seeking a divorce or khulʿ. If the divorce is in exchange for a financial compensation paid by the woman, then it is khulʿ, and it does not require the return of the full mahr (dowry); rather, it is according to their agreement. As for the furniture left by the husband in the apartment, it is his property, unless he explicitly gifted it to his wife, or if custom dictates that it is part of her mahr. It is preferable to consult the husband regarding the furniture to avoid future disputes.