All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
Our answer to your question is summarized as follows:
Firstly: Assuming Ihraam from Mina on the 9th of Thul-Hijjah is valid if you were residents in Makkah before assuming it, but if you came from outside Makkah for the Hajj, then in principle you were obliged to assume Ihraam from the Meeqaat. So if you delayed assuming Ihraam and you did so in Makkah – whether it is in Mina or elsewhere – then each one of you is obliged to offer a sacrifice due to abandoning one of the obligations of Hajj, which is assuming Ihraam from the Meeqaat.
The sacrifice is to slaughter a sheep or one-seventh of a cow or camel, which must be slaughtered in Makkah and distributed (its meat) to the poor of the Haram [of Makkah]. If you had already left Makkah, then you may appoint someone in Makkah to slaughter on your behalf.
Secondly, your leaving Muzdalifah on the night of the 'Eed after midnight: there is nothing wrong with this, Allah willing. Ibn Qudaamah said, “Whoever spends the night in Muzdalifah, it is not sufficient (i.e. acceptable) for him to leave before midnight, and if he leaves after midnight, then there is no harm on him. This is the view of Ash-Shaafi’i. Imaam Maalik said, 'If he passes by it [Muzdalifah] but does not stay in it, then he is obliged to offer a sacrifice. In case he stays in it, then he is not obliged to offer a sacrifice, and he may leave whenever he wishes.'”
The sufficient period of staying overnight in Muzdalifah is achieved even by staying for a little while after midnight. An-Nawawi said, “The correct view that is stated in Al-Umm is that this staying overnight in Muzdalifah is achieved by staying for a while in the second half of the night...”
What is taken into account is the middle of the night, regardless of whether the middle of the night is before or after 2:00 AM. The middle of the night is known by calculating the time between sunset and the break of dawn, so if half of this time has passed, then the middle of the night has passed.
Thirdly, your throwing of the Jamaraat at 2:30 AM is correct – Allah willing – if this happened after the middle of the night, because, according to the view of a group of scholars, the time of throwing the Jamaraat on the day of 'Eed starts after the middle of the night. Ibn Qudaamah said:
“As regards the time of permissibility, then the beginning time is the middle of the night of the day of sacrifice [first day of 'Eed]. This is the view of ‘Ataa’, Ibn Abi Layla, ‘Ikrimah ibn Khaalid and Ash-Shaafi’i… Our evidence is what was reported by Abu Daawood from ‘Aa’ishah, may Allah be pleased with her, who related that 'the Prophet ordered Umm Salamah the night of the sacrifice and upon his order, she threw Jamrat Al-‘Aqabah before dawn, and then she performed Tawaaf Al-Ifaadhah. It was also reported that he ordered her to hasten in performing Tawaaf Al-Ifaadhah and go to Makkah after the Fajr prayer.' Imaam Ahmad provided this as evidence. We have already mentioned in the hadeeth of Asmaa’ that she threw the pebbles (of Jamrat Al-‘Aqabah) and then went back and prayed the Fajr prayer.”
Fourthly, throwing the pebbles on the days of Tashreeq before the Thuhr prayer is not valid according to the majority of the scholars, as they hold the opinion that it is absolutely not permissible to throw the pebbles before the sun has reached its meridian [i.e. the time of the beginning of the Thuhr prayer]. Some scholars, however, permitted throwing the pebbles on the third day of Tashreeq before the sun is at its meridian, and some permitted it on the second day of Tashreeq, and some permitted it on any day of the days of Tashreeq. The preponderant view that we adopt here at Islamweb is the view of the majority of the scholars, because the Prophet threw the pebbles after the sun was at its meridian, and he said, “Take your rituals from me (i.e. perform your rituals in the same manner as you see me performing them).” If throwing the pebbles before the sun is at its meridian had been permissible, the Prophet would have done it or permitted the Companions to do it in the same manner that he had given them permission to start going away from Muzdalifah after the middle of the night, as it is better to perform an act of worship at its beginning time on the one hand, while making it easy for the pilgrims on the other.
Therefore, your throwing of the pebbles before the sun was at its meridian is not sufficient for you. Hence, you are obliged to offer a sacrifice for having abandoned one of the obligations of Hajj, which is throwing the pebbles on the days of Tashreeq. The Fiqh Encyclopedia reads, “The Shaafi'i and Hanbali Schools are of the view that a person who did not throw the pebbles at all, or who did not throw the pebbles for one or two days, or who left out three pebbles while throwing any of the Jamaraat, must offer a sacrifice …”
The sacrifice, as we have mentioned earlier, is to slaughter a sheep or one-seventh of a camel [or a cow], which must be slaughtered and distributed to the poor of the Haram [of Makkah].
Fifthly, your saying, “We were not able to stay in Mina during these two days;” if you mean that you did not stay in it for most of the night, then in that case you have left out another obligation of the obligations of Hajj, which is to stay overnight in Mina.
The Fiqh Encyclopedia reads:
“The majority of the scholars – among whom are the scholars of the Maaliki, Shaafi’i and Hanbali Schools of jurisprudence, ‘Urwah, Ibraaheem, and ‘Ataa’ – are of the view that it is an obligation to stay overnight in Mina during the nights of Tashreeq, and a person who abandons this without having a sound reason must offer an expiation, which is to offer a sacrifice, due to not staying most of the night, according to the Maaliki school, or for abandoning the staying overnight completely, according to the Shaafi’i and Hanbali Schools. For failing to stay one night, one must offer a Mudd (750ml) of food, and for failing to stay two nights, one must offer two Mudds, according to the Shaafi’i and Hanbali Schools…”
Nonetheless, if you did not stay overnight in Mina due to a sound reason, such as if you were prevented, or due to the need of the pilgrims for your service, then we hope that you are exempted from offering a sacrifice because if a pilgrim abandons staying overnight in Mina due to a sound reason, then he is not obliged to offer a sacrifice.
The Fiqh Encyclopedia reads:
“If a pilgrim abandons staying overnight for a sound reason, then he is not required to do anything, such as the people who were appointed by Al-‘Abbaas to provide water to the pilgrims, and those who were guarding camels, then they are entitled to refrain from staying overnight in Mina without being obliged to offer a sacrifice; the like of them is one who fears about a soul or wealth, or who cannot abandon a sick person because there is no one else to take care of him, or who learns of the death of a relative in their absence…”
Allah knows best.