Who is the one deemed "able" (al-qādir), for whom the uḍḥiyah (sacrificial offering) is sunnah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The one who is deemed "able" (al-qādir) [to perform the uḍḥiyah, i.e., the sacrifice] is someone who possesses wealth sufficient to acquire the sacrificial animal, over and above what is needed to cover his own living expenses and the living expenses of his wife and children — or of anyone else whose financial support (nafaqah) is legally obligatory upon him — for the day of ‘Eid and the three days of Tashrīq [that follow it], since this is the designated time period for the sacrifice. And Allah, the Exalted, knows best.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
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.
Who is the "Capable Person" for whom the Udhiyah is recommended?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The "Capable Person" (Al-Qadir): This refers to anyone who possesses surplus wealth beyond their own essential needs and the financial maintenance of their wife, children, or whoever is under their legal care, during the day of Eid and the three days of Tashreeq (the 11th, 12th, and 13th of Dhul-Hijjah), as this is the designated timeframe for the sacrifice. And Allah Knows Best.