Is carrying a deceased father in a wrong way that led to his death considered killing or causing his death, and what are the consequences of that?

What you did, lifting your father, and his subsequent death, falls into two categories:

1. If doctors confirm that the lifting was the cause of death: This is considered accidental killing, and expiation (fasting for two consecutive months) is obligatory for everyone who participated in lifting him. As for the blood money (Diyah), a single Diyah is obligatory upon you, unless the rest of the heirs pardon it. 2. If doctors confirm that the lifting was not the cause of death, or if they are in doubt about it: Then neither Diyah nor expiation is obligatory upon you, because the default is innocence, and liability is not established by doubt, as Ibn Hazm mentioned.

Determining the cause depends on the report of at least two trustworthy doctors who agree on the cause of death.