Mourning for a Non-Jewish Parent

Q: Should a convert mourn for his non-Jewish parent?
A: One should mourn in the accepted manner of mourning by non-Jews over their parents in that place, in order that people do not say that one went from a higher level of holiness to a lower level. Acting in this way is ethical. He is not obligated to mourn with all of the Halachot as one does for a Jew. However, when Tavi, Rabban Gamliel's servant, died, Rabban Gamliel accept consolation, as if he were Jewish. When asked about this, he responded: Tavi is not like other servants, he is kosher (Mishnah Berachot 2:7). Therefore, he is not obligated to sit shiva for them, but he may do so. It is a personal decision (see also Shut Igrot Moshe, Yoreh Deah 2:130).
Q: Should he recited Kaddish?
A: Ha-Rav Ovadiah Yosef rules that it is permissible and proper to recite Kaddish (Shut Yechaveh Da'at 6:60).