What is the ruling concerning my Hajj, given that I circumambulated the Kaaba for most of the rounds but left out the Al-Hijr (the separating wall adjacent to the Kaaba from the northern side)?

If the circumambulation (Tawaf) was Tawaf al-Ifadah, then it is invalid and must be repeated for the Hajj to be sound. This is done by returning to the Sacred Mosque and performing seven circuits around the Kaaba, outside of the Hijr of Isma'il. However, if it was the farewell circumambulation (Tawaf al-Wada'), then the pilgrim must offer a sacrifice (dam) to be slaughtered in Mecca for the poor, and returning to the Sacred House does not suffice for the blood sacrifice. If the circumambulation was a supererogatory act (nafilah), then there is nothing incumbent upon the pilgrim.