Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?
The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.
What is the ruling on performing Tahajjud after the Witr?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for one who has prayed the Witr to perform voluntary (Nafl) prayers after it. However, it is preferable for the Witr to be the final prayer of the night. Therefore, if a person is confident that they will wake up during the night for Tahajjud, it is recommended for them to delay the Witr until after the Tahajjud. Conversely, if one fears they may not wake up, they should perform the Witr before sleeping.
Al-Khatib al-Shirbini (may Allah have mercy on him) stated: 'It is not disliked (Makruh) to perform Tahajjud after the Witr, but it is not recommended to do so intentionally.' [Mughni al-Muhtaj, Vol. 1/P.454]. And Allah the Exalted knows best."
Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
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, rump, or udder due to being cut off. This is in contrast to an animal that was naturally born without a tail, rump, or udder; such an animal is valid for sacrifice. And Allah the Almighty knows best.