What is the ruling on asking for mercy upon a disbeliever (kaafir) and praying over them, and is that considered a sin or an act of disbelief (kufr), and what is the most authoritative opinion on this matter?

To invoke Allah’s mercy upon a disbeliever and to pray for them are forbidden acts, by scholarly consensus, and constitute an transgression in supplication. This is based on the Almighty’s saying: "It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire." Some scholars have even considered this act to be disbelief because it implies a denial of what Allah has informed us in definitive texts, that Allah does not forgive that partners be associated with Him. However, declaring someone an apostate has specific conditions and impediments determined by scholars. A Muslim must acquire deep understanding of their religion and be wary of acts that lead to apostasy.