He intended to perform Qiran Hajj but did not sacrifice the Hady and performed Tawaf-ul-Wada` before completing performing the rituals

Q: Ten years ago, I performed Hajj with my parents, uncle and brother. Some things happened to us and we are in doubt about them; we said Talbiyah (devotional expressions chanted at certain times during Hajj and `Umrah) for Qiran Hajj (combining Hajj and `Umrah without a break in between). We reached Makkah and performed Tawaf-ul-Qudum (circumambulation of the Ka`bah on arrival in Makkah) and Sa`y (going between Safa and Marwah during Hajj and `Umrah), and then we went to Mina and stayed overnight there. This was on the sixth day of Dhul-Hijjah. We remained in Ihram (ritual state for Hajj or `Umrah) and did not perform Tahallul (removal of the ritual state for Hajj and `Umrah) on the morning of the Day of `Arafah (9th of Dhul-Hijjah). We performed Fajr (Dawn) Prayer in Mina, and then we moved to `Arafah where we stayed until sunset. After that, we proceeded to Muzdalifah, and offered the Maghrib (Sunset) and `Isha' (Night) Prayers, (Part No. 10; Page No. 393) combining or shortening them. Then, we collected pebbles and as we had our parents with us, we continued walking after midnight until we reached Mina, where we stoned Jamarat-ul-`Aqabah (the closest pebble-throwing area to Makkah). Then, we continued walking to Makkah, where we performed Tawaf-ul-Ifadah (final obligatory circumambulation of the Ka`bah in Hajj) and Sa`y, then we returned to perform Tawaf-ul-Wada` (circumambulation of the Ka`bah on leaving Makkah), after which we returned to Mina, where we stayed for the 11th and 12th of Dhul-Hijjah. After that, in the afternoon, we left Mina to our country. Your Eminence Shaykh! When we reached Mina, we asked some seekers of knowledge and they answered us that we do not have to offer Hady (sacrificial animal offered by pilgrims) and that it is permissible to perform Tawaf-ul-Wada` along with Tawaf-ul-Ifadah. However, we were not convinced with this opinion so we went to a learning circle in Al-Khif Masjid in Mina, and waited till the Shaykh finished preaching and asked him whether we should offer Hady when we are Qarins (pilgrims combining Hajj and `Umrah without a break in between) and did not perform Tahallul. We also asked him whether it was permissible to offer Tawaf-ul-Ifadah along with Tawaf-ul-Wada`. His answer was the same, meaning that this is permissible, but that the better way is to perform Tamattu` Hajj (`Umrah during the months of Hajj followed by Hajj in the same year with a break in between) and offer Hady.Our question is: Is our Hajj valid? Is the obligation of offering Hady waived, or should we offer it, and if we should, how can we do this? Please guide us. May Allah reward you with the best!