A man insulted the Divine Essence; is it obligatory for him to perform Ghusl?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Insulting or blaspheming the Divine Essence (Dhat al-Ilahiyyah) constitutes apostasy (Riddah). The perpetrator of this grave sin must immediately repeat the two testimonies of faith (Shahadah) and sincerely repent to Allah the Exalted. It is recommended (Sunnah) for them to perform a ritual bath (Ghusl), though it is not a mandatory condition [for the validity of their return to Islam]. And Allah the Exalted knows best.
Should a person who doesn’t offer Tasbeehb (saying Subhaana Rabbiya Al-‘Atheem during Rukoo`, and saying Subhaana Rabbiya Al-A‘laa during Sujood) during Rukoo` and Sujood perform As-Sahw Sujood (prostration of forgetfulness)?
He/ she doesn`t have to perform Sujood As-Sahw, whether he/she didn`t offer Tasbeeh during Rukoo` and Sujood either intentionally ,or unintentionally, provided that the attentiveness of the heart wasn`t undermined since it is a pillar in both.
Do ear and nose drops break the fast?
Yes, ear and nose drops break the fast because both the nose and ears are open passages to the body cavity.
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.