Is the divorce valid in the aforementioned situation, and what is the ruling on the wife remaining with her husband after this divorce?

The intellect is the basis of accountability. If it is lost, a person's eligibility for accountability is removed, as the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: from the insane person whose mind is overwhelmed until he recovers..." If your father acts while his mind is overwhelmed due to possession or old age, he is not accountable, and his divorce does not count. It is recommended to continue with Ruqyah (Islamic exorcism) and advise your father to be diligent in acts of worship, reciting the Quran, and performing dhikr (remembrance of Allah).