Is it permissible to give to the poor from among the People of the Book from the Udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to give to the poor among the People of the Book from a voluntary sacrifice (uḍḥiyyat taṭawwuʿ), just as it is permissible to give charity (ṣadaqah) to them. This opinion is a view (wajh) within the Shāfiʿī school, which was favored by al-Muḥibb al-Ṭabarī and Imam al-Nawawī. [See: Ḥāshiyat Ibn Qāsim al-ʿAbbādī ʿalā Tuḥfat al-Muḥtāj (Vol.9/P.365)]. And Allah Almighty knows best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
Is it recommended (mustaḥabb) for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from its meat?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is recommended (mustaḥabb) — not obligatory — for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from it. Allah Almighty says {what means}: "So eat from them and feed the desperate (qāniʿ) and the beggar (muʿtarr). Thus We have subjected them to you that you may be grateful."— [Sūrat al-Ḥajj (22): 36]
Explanation of terms:
Al-Qāniʿ — the poor person who does not ask people for money, food..eccetera.(beg)
Al-Muʿtarr — the poor person who does ask people for money, food..eccetera (begs)
And Allah Almighty knows best.
What are the Sunnahs and etiquettes recommended for the person offering the Udhiyah?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
There are several Sunnahs (prophetic traditions) and etiquettes that are highly recommended for the person offering an Udhiyah (sacrificial offering) to observe:
First:
It is a Sunnah for anyone intending to offer a sacrifice to refrain from cutting or removing any of their hair or nails once the first ten days of Dhul-Hijjah begin. This is based on the statement of the Prophet (peace and blessings be upon him): "When the ten days [of Dhul-Hijjah] begin and one of you intends to offer a sacrifice, let him not touch any of his hair or skin." (Narrated by Muslim)
However, if someone does happen to remove any hair or nails, they have not committed a sin, and their sacrifice remains perfectly valid.
Second:
The person offering the sacrifice should ideally slaughter the animal themselves. If they are unable to do so, they should at least witness its slaughter. This is drawn from what our Master, the Messenger of Allah (peace and blessings be upon him), said to Lady Fatima (may Allah be pleased with her):
"Stand up and witness your sacrifice, for with its very first drop of blood, every sin you have committed will be forgiven." (Narrated by Al-Tabarani in his Mu'jam, Al-Hakim in his Mustadrak, and Al-Bayhaqi in his Sunan)
Third:
Face the Qiblah (the direction of prayer) at the time of slaughtering, as the Qiblah is the most honorable of directions.
Fourth:
Pronounce the name of Allah (Tasmiyah) at the moment of slaughter by saying: "Bismillah ar-Rahman ar-Rahim" (In the Name of Allah, the Most Gracious, the Most Merciful). Even if one forgets to say it, the meat remains lawful (Halal) to eat. Allah, Blessed and Exalted is He, says:
"So eat of that [meat] upon which the name of Allah has been mentioned." (Al-An'am: 118)
It is also recommended to send blessings upon our Master, the Messenger of Allah (peace and blessings be upon him), and to follow it with the Takbeer (Allahu Akbar).
Fifth:
Supplicate for acceptance by saying: "Allahumma hadhihi minka wa ilayka, fa-taqabbal minni" (O Allah, this is a blessing from You and is offered back to You, so please accept it from me). This means: This sacrifice is a blessing that originated from You, and I am offering it to draw closer to You. And Allah the Almighty Knows Best.