Is a convert obliged to honor his parents? I understand that a convert loses all halakhic relationship to his parents upon being "reborn." Therefore, does the mitzvah of kibud av va'eim still apply?
הגר אסור לקלל אביו העכו"ם ולהכותו. ולא יבזהו כדי שלא יאמרו באו מקדושה חמורה לקדושה קלה שהרי זה מבזה אביו. אלא נוהג בו מקצת כבוד.
A convert is prohibited from cursing his non-Jewish father or hitting him. And he shouldn't disgrace him, so that people shouldn't say that the converts came from greater holiness to lesser holiness by converting, since behold this one is disgracing his father. Rather, the convert should treat his parents with at least some honor.
The basis for this, as explained in Igros Moshe and elsewhere, might be that honoring parents is a logical mitzvah which is incumbent upon and practiced by all people, Jew and non-Jew, thus one must continue honoring biological parents after conversion, since logic dictates that one owes his parents an enormous amount.