Is it permissible for a woman over sixty not to wear a hijab in front of her deceased husband's grandson (her step-grandson), who is not more than fifteen years old, and to shake his hand or kiss him?

The son is a mahram (definition) to the woman because she is his maternal grandfather's wife. It is forbidden for a man to marry his father's or grandfather's wife, no matter how distant the lineage, whether the grandfather is on the paternal or maternal side. This is based on the Almighty's saying: "And do not marry those [women] whom your fathers married, except what has already occurred. Indeed, it was an immorality and hateful [to Allah] and was a terrible way."

As for kissing, the woman may kiss the son if there is no fear of fitna. It is preferable that the kiss be on the forehead or head, while avoiding the mouth or cheek, except in specific cases, such as a father with his daughter.