Is it permissible for those offering condolences to say, "May He forgive your deceased female (relative)" after "May Allah magnify your reward and ease your bereavement," and is it permissible to say, "To the soul of the Prophet, peace and blessings be upon him and his family, and to the soul of the deceased, Al-Fatihah"?

Using the phrase "marḥūmatukum" (your deceased woman) for a deceased woman is permissible if it is said with the intention of hope or supplication. However, if it is said as a statement of fact that she has been shown mercy, then it is not permissible, because it involves testifying to mercy without knowledge. Sheikh Ibn Uthaymeen clarifies that words like "al-marḥūm" (the one shown mercy) or "al-maghfūr lahu" (the one forgiven) are not permissible if said as a statement of fact, due to the lack of knowledge concerning the attainment of mercy or forgiveness. However, if they are said as a supplication and a hope that Allah may have mercy on him, then there is no objection. It is most probable that the speaker's intention is hope, optimism, and supplication.