What are the Sharia consequences when the sacrificial time for the uḍḥiyyah comes to an end?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the sun sets on the final day of Tashriq (the 13th of Dhu al-Hijjah) and the Udhiyah (sacrificial animal) has not yet been slaughtered, its designated time has expired. Should a person slaughter it after this point, it will not be counted as an Udhiyah.
However, if the sacrifice was a vowed one (Mandhurah), they are strictly obligated to slaughter it as a makeup act (Qada’), and its meat must be distributed entirely according to the rules governing vowed sacrifices.
It is stated in Bushra al-Karim (p. 702): "If one slaughters after sunset on the final day [of Tashriq]... it does not count as an Udhiyah, unless it was a vowed sacrifice, in which case it is fulfilled as a makeup act (Qada’)." And Allah the Almighty Knows Best.
What is the ruling on sacrificing a hornless sheep?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is valid to sacrifice a hornless sheep (al-Jamma’ or al-Jalha’). Similarly, a sheep with a broken horn is also acceptable; it does not affect the validity of the sacrifice even if the break causes bleeding, unless the injury is so severe that it leads to the spoilage of the meat. And Allah the Almighty knows best.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
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.