then certainly a proselyte may say Qaddish for a Gentile father who is naturally following the religion in which he was brought up. So, too, Abraham Zvi Klein, a rabbi in Hungary (Beerot Avraham Il), speaks of receiving a gift from a Gentile woman who wants her name memorialized(i.e., not even a relative of a convert), and he concludes:"There is no prohibition against recording her name and her good deed in the Hevra Qadisha, and we should recite an El male rachamim’ for her on Yizqor days."
As for the second question, there is some sort of justification for an objection on the part of the man, or of his second wife, to his first wife(and possibly also her relatives) being memorialized now the man is married to this second woman. This question has come up quite often in the literature and has been dealt with in Reform Responsa, p. 162. For example, Eleazer Deutsch(1850-1916) in his Duda-ei Hasadeh, 14, was asked whether a remarried man may recite Yizqor for his first wife. He says no, but that if it was the custom of the synagogue- as it is in some communities- for the cantor to read a list of all the names memorialized, there was no objection to the remarried man being present. The general conclusion of all who discussed the question is that such memorial rites as might occur at home(the Yahrzeit light, etc.) should certainly not be observed any more. In the synagogue, however, if there is no one to say Qaddish for his first wife, the husband may do so. Of course, if there are children, it is better that they should say Qaddish. In the question asked, the names include not only the name of the first wife, but those of her relatives, so the second wife can have less objection to their names being read than if it were the first wife's name alone. Furthermore, there are grandchildren who want to honor their grandparents, which certainly should be permitted.