Can an Udhiyah be made up if its time is missed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the sacrificial animal (udhiyah) is a voluntary (nafl) offering and its prescribed time is missed after the three days of Tashriq have ended, then it is not to be made up as a sacrifice; rather, it becomes merely a sheep for meat.
However, if it was a vowed (nadhr) sacrifice and its time is missed, then it must still be slaughtered, and the slaughtered animal is to be treated as it would have been during its prescribed lawful time. And Allah Almighty knows best.
Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
It is permissible for someone who sacrificed on behalf of another with their permission to eat from it with their permission, and they stand in their place (act as their representative) in distributing it.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.8/P.141): "And he—meaning the one sacrificing on his own behalf, provided he has not apostatized—has the right to eat from a voluntary sacrifice and his sacrificial gift; rather, it is recommended. As for an obligatory sacrifice, it is forbidden for him to eat from it, whether it was designated as such initially or as a liability in his dhimmah. And excluded by what has preceded is if he sacrifices on behalf of another, or if he apostatized, then it is not permissible for him to eat from it, just as it is absolutely impermissible to feed a disbeliever from it."(The text I found indicates the impermissibility of eating) ???
And it is stated in Hashiyat al-Jamal ‘ala Sharh al-Manhaj (Vol.5/P.262): "If a person offers a sacrifice on behalf of a living person with their permission, does he act as their representative in distributing it—on the grounds that permission to sacrifice is permission to distribute it—or does it depend on their explicit permission? This requires consideration, but the first view is not far-fetched." And Allah the Almighty knows best.
What is the wisdom behind legislating the Udhiyah?
The Muslim must know that through the Uḍḥiyah, he complies with the command of Allah, the Exalted, and performs a worship that brings him closer to Allah and distances him from the Fire.
The Uḍḥiyah holds profound wisdoms and noble meanings, including:
1-Reviving the Sunnah of Abraham, peace be upon him: He complied with Allah's command when He ordered him to slaughter his son Ishmael. Abraham, peace be upon him, succeeded in the test, and when he was about to slaughter his son, Allah sent down a ram to ransom Ishmael and commanded him to slaughter it instead. Allah, the Exalted, says {what means]: "And when he reached with him [the age of] exertion, he said, 'O my son, indeed I have seen in a dream that I [must] sacrifice you, so see what you think.' He said, 'O my father, do as you are commanded. You will find me, if Allah wills, of the steadfast.' And when they had both submitted and he put him down upon his forehead, We called to him, 'O Abraham, You have fulfilled the vision.' Indeed, We thus reward the doers of good. Indeed, this was the clear trial. And We ransomed him with a great sacrifice." [Al-Ṣāffāt/102-107]. Thus, the sacrificial offering became an enduring Sunnah until the Day of Judgment, and Muslims offer their wealth as sacrifices, drawing closer to Allah, the Exalted, reviving this great Sunnah.
2-Providing abundance for people on Eid day and the Days of Tashrīq: Among the wisdoms of the Uḍḥiyah is that the Muslim provides generously for his family, neighbors, relatives, and the poor during these days. The Muslim is encouraged to eat from his sacrifice, give charity from it to the poor, and gift from it to his wealthy neighbors. Thus, goodness spreads throughout the entire community. The Prophet, peace and blessings be upon him, said: "The Days of Tashrīq are days of eating and drinking." (Narrated by Muslim). Allah, the Exalted, says {what means}: "And the camels and cattle We have appointed for you as among the symbols of Allah; for you therein is good." [Al-Ḥajj/36]. This good includes the good of both this world and the Hereafter.
A man led the people in prayer as imam, and at the end of the prayer he performed a prostration of forgetfulness (*sujūd al-sahw*) because he had omitted a short *sūrah* after al-Fātiḥah. What is the ruling on his prayer and that of those praying behind him?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
According to the Shāfiʿī school, it is sunnah to recite a sūrah after al-Fātiḥah in the prayer. One who omits it has a valid prayer, and no prostration of forgetfulness (sujūd al-sahw) is prescribed for omitting it. If someone performs sujūd al-sahw for its omission while knowing the ruling and remembering it, his prayer is invalidated. But one who is ignorant of the ruling, or who did so out of forgetfulness, his prayer is not invalidated, because this is among the matters that are obscure to people, and ignorance of it is not restricted to those who recently entered Islam.
Shaykh al-Islām al-Shams al-Ramlī said in Nihāyat al-Muḥtāj ilā Sharḥ al-Minhāj (Vol.2/p.70): “The remaining sunnahs are not compensated for by prostration, such as the remembrances (adhkār) of bowing and prostration, that is, the opening supplication (duʿāʾ al-iftitāḥ) and the sūrah, in accordance with the base rule, because they are not of the same nature as what has been reported [as compensable]. If one prostrates for any of them deliberately, his prayer is invalidated, unless he is excused due to ignorance. As for the objection raised that the ignorant person does not know that sujūd al-sahw is prescribed, and whoever knows it knows its place, this is refuted by denying such a necessary connection, for the ignorant person may hear only that sujūd al-sahw is prescribed before the salām, and so assume that it applies to every sunnah and is not restricted to its prescribed place.”
This is among the matters that are obscure, in which the mukallaf is excused for ignorance, as stated by al-Shabrāmallisī in his Ḥāshiyah ʿalā Nihāyat al-Muḥtāj (Vol.2/p.70).
However, if the imam prostrates, and the follower (maʾmūm) presumes that his imam’s prostration is for a reason for which one does not prostrate, it is not permissible to follow him in it, so long as the follower knows the ruling.
Accordingly, the prayer of one who did not recite a sūrah after al-Fātiḥah is valid, and sujūd al-sahw is not prescribed for it. Whoever prostrates out of ignorance or forgetfulness, his prayer is valid, because this is among the issues hidden from the general public. But whoever prostrates while knowing the ruling and remembering it, his prayer is invalidated. And Allah Almighty knows best.