What is the ruling on supplicating for the deceased at a house of mourning, and what is the ruling on the action of the female preacher who permitted it and claimed it to be lawful?

If the question refers to gathering at a mourning house to supplicate for the deceased, recite the Qur'an, and similar acts, then this is an innovated Bid'ah that neither the Prophet (peace be upon him) nor his noble companions practiced. Sheikh Ibn Baz was asked about gathering at the deceased's house for three days for prayer and supplication, and he replied that gathering at the deceased's house for eating, drinking, and reciting the Qur'an is an innovation (Bid'ah). Similarly, praying at home is not permissible; rather, men should pray in the mosque with the congregation. People should visit the family of the deceased to offer condolences, supplicate for them, and ask for mercy upon their deceased. However, gathering to hold a mourning ceremony with specific recitations or supplications is an innovation (Bid'ah).