Is shaking hands with a non-mahram, embracing him, kissing him, or engaging in indecent acts with him considered Zina (fornication/adultery), or are these different degrees [of sin]? And what is the ruling on a woman embracing an elderly non-mahram man under the pretext that he views her as his daughter?

The fatwa (definition) is that it is forbidden for a man to shake hands with a non-mahram (definition) woman. This is one of the preludes to zina (illicit sexual intercourse) which the Sharia (definition) has prohibited, even if it is not zina itself. These preludes have been metaphorically called zina in the Prophetic hadith (definition), such as the gaze of the eye, the listening of the ear, the speech of the tongue, the striking of the hand, and the stepping of the foot. These preludes differ in their sinfulness, but they are all strongly prohibited, and touching a non-mahram woman is the most dangerous among them. Therefore, it is not permissible to shake hands with, embrace, or kiss a non-mahram man, and there should be no leniency in this matter under the pretext of shyness or any other excuse.