Can one supplicate for a deceased disbelieving father afflicted with untreated bipolar disorder who used to call others to disbelief? And is the pen lifted from him due to his illness?

The sick person is not exempt from accountability and religious obligations unless they lose their mind. It is not permissible to supplicate for a disbeliever, nor do they benefit from righteous deeds, as Allah the Almighty says: "It is not for the Prophet and those who have believed to ask forgiveness for polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire." As for one who outwardly professes Islam, they are not to be judged as a disbeliever except by a judicial ruling, and it is permissible to supplicate and seek forgiveness for them. The way out is to offer supplication and seek forgiveness conditionally, such as saying: "O Allah, if my father was a Muslim, then have mercy on him."