It is not for the Prophet, and those who believe, to pray for the forgiveness of idolaters even though they may be near of kin (to them) after it hath become clear that they are people of hell-fire.
Times are computed by method; your mosque's timetable governs the adhan. Every text carries its source and grade. Nothing here is a fatwa, a prediction, or a substitute for a doctor: your own scholar decides what is contested, and the tradition itself says the practice is alongside treatment, never instead of it.