What are the conditions for the validity of the slaughtering process according to Sharia?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the Sharia-mandated conditions for the validity of the slaughtering process (Adh-Dhabh), they are as follows:
The Identity of the Slaughterer: The person performing the slaughter must be either a Muslim or from the People of the Book (Christian or Jewish).
The Required Cuts: Both the trachea (windpipe/breathing passage) and the esophagus (food passage) must be completely severed.
Stability of Life: The animal must possess stable life at the start of the slaughtering process. This is identified by clear signs, such as vigorous movement or the forceful gushing of blood after the throat and esophagus are cut.
The Tool of Slaughter: The tool used must be sharp, capable of cutting or piercing by its edge and not by its sheer weight or blunt force.
And Allah the Almighty knows best.
Is it obligatory to have an intention (niyyah) for every prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is obligatory for the worshiper to have a specific intention (Niyyah) for every prayer, meaning they must consciously intend the act of worship they are performing. The intention is a pillar (Rukn) of the prayer, and the prayer is not valid without it. It is not a requirement to utter the intention verbally; rather, doing so is considered a recommended Sunnah. And Allah the Exalted knows best.
What is the ruling of Islamic Law on supplicating with other than the transmitted (Ma'thur) supplications in prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to supplicate (make du'a) during the prayer for anything from the affairs of religion or worldly life, and the prayer is not invalidated by doing so.
Shaykh al-Islam, the Imam an-Nawawi, may Allah have mercy on him, says: "Our madhhab [i.e., the Shafi'i madhhab] holds that it is permissible for a person to supplicate during it [the prayer] with anything that is permissible to supplicate with outside the prayer, from the affairs of religion or worldly life. He may say: 'O Allah, grant me wholesome sustenance, offspring, a house, and a beautiful young wife' — describing her; or: 'O Allah, free so-and-so from prison,' or 'destroy so-and-so,' and other such things — and none of this invalidates his prayer according to us. And this is also the view of Malik, ath-Thawri, Abu Thawr, and Ishaq." [Al-Majmu', Vol.3/P.454]. And Allah, the Exalted, knows best.
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.