What are the categories of the livestock permissible for Udhiyah?
Praise be to Allah, and peace and blessings be upon the Messenger of Allah.
The Udhiyah (sacrificial offering) is not valid except from Al-An’am (livestock), which are: camels, cattle, and sheep/goats. Allah the Almighty says {what means}: "And for every nation We have appointed a rite [of sacrifice] that they may mention the name of Allah over what He has provided for them of beast-livestock." [Al-Hajj/34]
The best of them are camels, then cattle, then sheep/goats. A sacrifice of a camel or a cow avails for seven people. Jabir (may Allah be pleased with him) said: "We sacrificed with the Messenger of Allah (peace and blessings be upon him) in the year of Al-Hudaybiyah a camel for seven and a cow for seven." [Narrated by Muslim] And Allah the Almighty knows best.
Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
What are the valid excuses for abstaining from congregational prayer in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Concessions (Rukhsah) are granted to abstain from congregational prayer in the mosque due to general excuses, such as: rain that causes hardship in going out, strong winds at night, heavy mud that cannot be traversed without the risk of soiling oneself, hot winds, and extreme heat or cold. There are also specific individual excuses, such as: illness that makes walking as difficult as walking in the rain, severe drowsiness, evident hunger or thirst, the suppression of bodily wastes (urine, stool, or gas), and fear for one's life, limb, physical faculty, wealth, or honor, among other valid excuses. And Allah the Exalted knows best.
What are the Sunnahs and etiquettes recommended for the person offering the Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
There are several Sunnahs and etiquettes that are recommended for the person offering the Udhiyah (sacrifice) to observe, including:
1. Refraining from Cutting Hair and Nails
It is Sunnah for the one intending to sacrifice to refrain from removing any hair or nails once the first ten days of Dhul-Hijjah begin.
The Prophet (peace be upon him) said: "When the ten days [of Dhul-Hijjah] begin and one of you intends to offer a sacrifice, let him not touch [remove] any of his hair or skin." [Narrated by Muslim].
If someone does remove any hair or nails, they have not committed a sin, and their sacrifice remains valid.
2. Performing the Slaughter Personally (or Witnessing it)
It is recommended for the person offering the sacrifice to slaughter the animal themselves. If they are unable to do so, they should witness the slaughter.
The Messenger of Allah (peace be upon him) said to Fatimah (may Allah be pleased with her): "Stand and witness your sacrifice, for indeed, with its first drop of blood, your [previous sins] are forgiven." [Narrated by Al-Bayhaqi and Al-Tabarani; it is classified as a weak (da'if) hadith].
3. Facing the Qiblah
The animal should be positioned to face the Qiblah at the time of slaughter, as the Qiblah is the most noble of directions.
4. Mentioning Allah's Name (Tasmiyah)
The slaughterer should say: "Bismillah ar-Rahman ar-Rahim" (In the name of Allah, the Entirely Merciful, the Especially Merciful). Even if one forgets to say it, the sacrifice is still permissible to eat.
Allah (Blessed and Exalted be 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 the Messenger of Allah (peace be upon him) and to say "Allahu Akbar" (Allah is the Greatest) after the Tasmiyah.
5. Supplicating for Acceptance
The slaughterer should pray for the sacrifice to be accepted by saying:
"O Allah, this is from You and for You, so please accept it from me." (Allahumma hadhihi minka wa ilayka, fataqabbal minni).
And Allah the Almighty knows best.