Who is the one required to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered by the guardian of the newborn — the one upon whom the child's financial maintenance is obligatory — provided he is financially capable of doing so. 'Alī ibn Abī Ṭālib, may Allah be pleased with him, reported: "The Messenger of Allah ﷺ performed the 'aqīqah for al-Ḥasan with one sheep." — Narrated by al-Tirmidhī. And Allah Almighty knows best.
What is the ruling on omitting the prostration of recitation?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The prostration of recitation (Sajdat al-Tilawah) is a Sunnah for both the reader and the listener. There is no sin in omitting it, though doing so results in missing a great reward. Muslim narrated from Abu Hurairah (may Allah be pleased with him) that the Prophet ﷺ said: 'When the son of Adam recites a verse of prostration and prostrates, Shaytan withdraws weeping, saying: "Woe to him! (and in the narration of Abu Kuraib: "Woe to me!") The son of Adam was commanded to prostrate and he prostrated, so Paradise is his; and I was commanded to prostrate and I refused, so the Fire is mine."'
Sheikh al-Islam Imam al-Nawawi (may Allah have mercy on him) stated: 'It is recommended to prostrate immediately after reciting or hearing a verse of prostration. If one delays it but the interval is short, he may still prostrate. However, if the interval is long, the opportunity is missed.' [Rawdat al-Talibin Vol.1/P.323].
Furthermore, the prostration of recitation becomes obligatory (Wajib) in congregational prayer if the Imam prostrates, out of the necessity of following him. And Allah the Exalted 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 are the conditions for a valid Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
First: The age of the animal must meet the Sharia requirements. These requirements vary depending on the type of sacrifice:
Camels: Must have completed five years and entered their sixth.
Cows: Must have completed two years and entered their third.
Goats: Must have completed two years and entered their third. As for Sheep, they must have completed one year and entered their second.
Some scholars have permitted goats that have completed one year and entered their second.
The Hanafi school, along with an opinion in the Maliki school, permits sacrificing sheep that are at least six months old, provided they are healthy and physically substantial. According to the Shafi’i school, it is permissible if the sheep sheds its front teeth (ajdha') before reaching one year [Al-Iqna’, by Al-Shirbini (Vol.2/P.588)].
Second: Soundness and freedom from defects. The animal must be free from any defect that causes a decrease in its meat or market value. This is based on the hadith narrated by Al-Bara' bin 'Azib, that the Prophet (peace be upon him) said:
"Four [defects] are not permissible in sacrifices: A one-eyed animal whose blindness is evident, a sick animal whose illness is evident, a lame animal whose lameness is evident, and an emaciated animal that has no marrow in its bones." [Reported by Abu Dawood and Al-Tirmidhi, who graded it as authentic].
These defects are detailed as follows:
Evident Lameness: It is not permissible to sacrifice a lame animal if the lameness is severe enough to prevent it from walking to the pasture or seeking food, as this leads to a decrease in its meat. However, slight lameness that does not hinder its grazing is overlooked.
Evident Blindness (One-eyed): It is not permissible to sacrifice a sheep, cow, or camel that has a white film over its eye blocking light, or one that has lost an eye entirely. Weak vision that does not affect its ability to eat does not prevent the sacrifice from being valid.
Evident Illness: An animal with a clear sickness that prevents it from eating or moving is not valid. This includes severe mange (Jarab) that spoils the meat.
Extreme Emaciation: An animal so thin that there is no marrow left in its bones is invalid. The standard for emaciation that invalidates the sacrifice is that which spoils the quality of the meat to the point that people would find it undesirable even in times of plenty.
Additional Considerations:
These are the defects mentioned in the Prophetic tradition, and any defect that causes emaciation or reduces the meat or value is compared to them by analogy. This includes animals that are mentally unstable (diseased), those with mange, or those with a missing ear. In contrast, a slit or pierced ear does not affect the validity of the sacrifice. And Allah the Almighty knows best.