Is it permissible for my father to marry my maternal grandfather's widow (my grandfather's second wife, not my mother's mother), and is she considered one of his unmarriageable kin, whether my grandfather is alive or after his death?

Your mother is a stepdaughter to your paternal grandfather's second wife. There is no objection, according to the majority of scholars, to your father marrying both of them, or marrying one after divorcing the other, because there is no prohibited degree of kinship between him and either of them through lineage or affinity. This is the view of the majority of scholars. Your grandfather's wife is not considered a mahram to your father, neither during your grandfather's lifetime nor after his death, unless another reason for prohibition exists, such as suckling.