Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
What is the ruling on eating from one`s Udhiyah?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The Udhiyah (sacrificial offering) is divided into two categories: the vowed sacrifice (Al-Mandhurah) and the voluntary sacrifice (Al-Tatawwu').
First: The Vowed Sacrifice (Al-Mandhurah)
This refers to a sacrifice that has become strictly obligatory due to a formal vow (Nadr). It is completely impermissible for the person offering it, or any members of their family whom they are financially obligated to maintain, to eat any of its meat or fat. Furthermore, it is unlawful for them to personally benefit from its hide, wool, or any other part of it. If they happen to eat any portion of it, the offerer is legally obligated to give an equivalent amount of meat or its monetary value to charity. (As noted in Tuhfat al-Muhtaj by Imam Ibn Hajar al-Haytami,Vol. 9/P.364).
Second: The Voluntary Sacrifice (Al-Tatawwu’)
This is a recommended, non-obligatory sacrifice. The person offering it is fully permitted to eat from its meat, distribute portions as charity to the poor, and give pieces as gifts to those who are well-off. However, it remains a mandatory requirement to donate at least a minor portion of it to charity; this should not be less than approximately half a kilogram of raw, uncooked meat. And Allah the Almighty Knows Best.
What is the ruling on swallowing phlegm while fasting?
If a fasting person intentionally swallows phlegm, their fast is invalid, as it is possible to avoid it.
However, if they swallow it unintentionally, their fast remains valid.
Phlegm is impure and should be avoided.
What is the ruling on sacrificing a castrated animal or one with a missing tail?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to sacrifice a castrated sheep; as it has been established that the Prophet (peace be upon him) sacrificed:
"...two large, fat, horned, white-and-black, castrated rams (Mawju'ayn—meaning having crushed testicles)." [Narrated by Ibn Majah in his Sunan].
It is not permissible to sacrifice an animal that is missing its tail, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, or udder; such an animal is valid for sacrifice. And Allah the Almighty knows best.