This excerpt is taken from Dr. Tariq Humayun Sheikh's book Eid ul-Adha.
Sacrificing on behalf of the deceased
The Messenger of Allah, peace be upon him, used to say in the prayer while sacrificing:
❀ "O Allah! Accept it on behalf of Muhammad, the family of Muhammad, and the nation of Muhammad."
Reference: (Sahih Muslim: 1966, 1967, 1965 Sunan Abu Dawood: 2792)
❀ "O Allah! This (sacrifice) is Your gift and for You alone, so accept it on behalf of Muhammad (peace be upon him) and his nation."
Reference: (Sunan Abu Dawood: 2795, Sunan Ibn Majah: 3121, Musnad Ahmad: 3/375)
Explanation:
If the deceased used to give charity and donations in the way of Allah, then it is permissible to give charity on behalf of the deceased. Therefore, it is also permissible to offer sacrifice on behalf of the deceased.
Slaughtering the sacrificial animal with one's own hand
It is preferable to slaughter the sacrificial animal oneself. The Prophet of Allah, peace be upon him, used to slaughter the sacrificial animal with his blessed hand by "Nahr" or "Dhabh."
Reference: (Sahih Bukhari: 5565, 7399 Sahih Muslim: 1967 Sunan Abu Dawood: 2792 - 2795 Sunan Tirmidhi: 1494, Sunan Ibn Majah: 3121)
Having the sacrifice slaughtered on one's behalf by someone else
The sacrificial animal can be slaughtered by someone else or by a butcher on one's behalf. During the Farewell Pilgrimage, the Prophet Muhammad ﷺ had 37 camels slaughtered by Sayyidina Ali رضي الله عنه.
Reference: (Sahih Muslim: 1218, Sunan Ibn Majah: 3074, Sunan Abu Dawood: 1764, Musnad Ahmad: 1/159)
It is not permissible to give the skin or meat of the sacrifice to the butcher as a fee
It is not permissible to give the butcher the meat or skin of the sacrifice as payment. The wage should be given separately.
Reference: (Sahih Bukhari: 1716, Sahih Muslim: 1317, Sunan Abu Dawood: 1769, Sunan Ibn Majah: 3099)
Sacrifice on behalf of the entire family
If living in the same house where food is cooked in one place, a sacrifice offered by the head of the household suffices for the rest of the family members.
Reference: (Sunan Ibn Majah: 3147, Sunan Tirmidhi: 1505)
Where should the knife be moved when slaughtering a goat or cow?
The place to slaughter a goat / kid, lamb, and cow is the throat and the esophagus.
Reference: (Sahih Bukhari: before Hadith 5510)
How should the camel sacrifice be performed?
It is Sunnah of the Prophet Muhammad ﷺ to make the camel or she-camel stand, tie one of its legs (left), and then slaughter it.
Reference: (Sahih Bukhari: 1713, Sahih Muslim: 1320, Sunan Abu Dawood: 1768)
Issue of the fetus in the belly of the sacrificial animal
If after slaughtering the sacrificial animal, a complete fetus comes out of its belly (and it is dead), the command of the Prophet Muhammad ﷺ is: "If you wish, you may eat it, for indeed slaughtering its mother is considered slaughtering it."
Reference: (Sunan Abu Dawood: 2828, Sunan Tirmidhi: 1476, Sunan Ibn Majah: 3199)
Explanation:
If a fetus comes out alive from the belly of the sacrificial animal, then to complete the sacrifice, it must also be slaughtered.
Forgetting to say Bismillah at the time of slaughter
If one forgets to say Bismillah at the time of slaughter, such an animal is halal, because the Ummah of Muhammad ﷺ is forgiven for forgetfulness and mistakes.
Reference: (Sunan Ibn Majah: 2043 - 2045)
Reference: Explanation:
Because the intention is purely to sacrifice for the pleasure of Allah.
The neck being severed at the time of slaughter
If the neck is severed due to the sharpness of the knife while slaughtering, there is no harm.
Reference: (Sahih Bukhari: before Hadith 5510)
Skins of Sacrificial Animals
The use of the skins of sacrificial animals is the same as that of Zakat. Sayyidina Ali (may Allah be pleased with him) narrates that the Prophet of Allah (peace be upon him) ordered him to give the bags and leather of the sacrifice as charity.
Reference: (Sahih Bukhari: 1707,1716 Sahih Muslim: 1310 Sunan Abu Dawood: 1769, Sunan Ibn Majah: 3099)
Can the meat of sacrifice be given to a non-Muslim?
The meat of sacrifice can be given to a non-Muslim, because Allah Almighty has said:
فَكُلُوا مِنْهَا وَأَطْعِمُوا الْقَانِعَ وَالْمُعْتَرَّ
"Then eat from it yourselves and feed the one who is content and the one who asks."
Reference: (22-Al-Hajj:36)