Spending the night at Mina on the ninth of Dhul-Hijjah

Q: Two years ago, I performed Hajj with my mother. We went to `Arafah on the ninth of Dhul-Hijjah. We headed off at 2:00 pm on the eighth of Dhul-Hijjah. We sat with the multitudes of pilgrims on the ninth until sunset. Then we joined the pilgrims to Muzdalifah. We arrived there at 7:30 pm and remained until 2:00 am. Then we went to Jamarat (stone pillars at which pebbles are thrown during Hajj, Jamarat Al-`Aqabah being the closest to Makkah). Afterwards, we headed off to Makkah where we performed Tawaf-ul-Ifadah (final obligatory circumambulation of the Ka`bah in Hajj) and Sa`y (going between Safa and Marwah during Hajj). Then we went back to Mina at 5:30 am. A couple accompanied us and the husband was a guide for us as he had performed Hajj more than once. Please explain to me whether our Hajj was performed correctly. Someone told us that we were wrong to leave before morning. After we returned from Makkah, we stayed at Mina for the three Days of Tashriq (11th, 12th and 13th of Dhul-Hijjah) during which we threw pebbles (at the stone pillars during Hajj) at noon. Then we returned to Makkah again to make Tawaf-ul-Wada` (circumambulation of the Ka`bah on leaving Makkah) which my mother could not perform because she was overtaken by menstruation. I kept her outisde Al-Haram (the Sacred Mosque in Makkah). My mother was terribly exhausted. Please inform us whether her Hajj is valid. If not, can I perform Hajj on her behalf since I have performed Hajj twice on my own behalf? If we are required to offer Fidyah (ransom), how can we do that? Do we have to offer it in Makkah or in our country?