What is the ruling on offering a sheep as a sacrifice (Udhiyah) if its fat-tail is sound, except that when it was young, the tip of its fat-tail was cut so that it would grow larger? And what is the ruling in case of doubt regarding the amount that was cut?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Cutting a minor, insignificant portion from the tip of an animal's fat-tail (al-alyah) to encourage it to grow larger is not considered a defect, and it does not prevent the animal from being valid for sacrifice (Udhiyah).
It is stated in Tuhfat al-Muhtaj (Vol.9/P.352): "There is some scholarly deliberation regarding the common practice of cutting the tip of the fat-tail so that it grows larger. It could potentially be likened to a partial cut of the ear—supported by the jurists' general rule: 'even if it is a small amount.' On the other hand, if it is an exceptionally minor cut, it might have no effect on validity. This is explicitly clarified by the juristic exception to the general rule, which states that cutting a tiny piece from a large limb causes no harm. This latter view is more well-founded.
Furthermore, I found that some scholars investigated this matter and concluded: 'It should not affect validity if a custom-sanctioned portion of its fat-tail is removed during its youth to make it grow larger and look better, just as castrating a male animal causes no harm.' However, applying this unconditionally contradicts the established texts of the jurists, as understood from what I have laid out; thus, the restriction I specified is what must be relied upon."
Similarly, it is mentioned in Nihayat al-Muhtaj (8/135): "If a small piece is cut from the fat-tail to help it grow larger, the most well-founded view is that the sacrifice remains valid, as was given in a formal legal verdict (Fatwa) by my father [Shihab al-Din al-Ramli], may Allah be pleased with him. This is proven by the jurists' maxim: 'The loss of a tiny piece from a large limb causes no harm.'"
In cases where there is doubt as to whether the portion cut was large or small, the animal is still deemed valid for sacrifice. It is noted in Hashiyat al-Shubramallisi ‘ala Nihayat al-Muhtaj (Vol.8/P.135):
"This matter requires careful consideration, but the closer and more correct view is that it is valid. This is because soundness is the default state for the animal from which the piece was cut, and it aligns with what usually occurs—namely, that the part removed to help the fat-tail grow larger is naturally very small." And Allah the Almighty Knows Best.
How does the person praying perform the prostration (Sujud)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is an act of Sunnah for the person praying to descend for prostration (Sujud) by placing their knees first, then placing their hands on the ground, and then placing their nose and forehead simultaneously. It is obligatory that the toes of the feet be on the ground, directed towards the Qibla. And Allah the Exalted knows best.
Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.
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.