What is incumbent upon the one offering the sacrifice if, after slaughtering the animal, they discover that one of its internal organs is damaged or diseased?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The presence of disease or defect in the internal organs of a sheep does not affect the validity of the sacrificial animal, unless the disease leads to the animal becoming emaciated and its meat becoming corrupted.
It is stated in al-Iqnā' (2/590) by Imam al-Shirbīnī: "The third disqualifying condition: an animal with a manifest illness — meaning one whose illness visibly results in emaciation and corruption of its meat. However, if the illness is minor and does not produce such effects, it doesn`t affect the validity of the sacrificed animal." And Allah Almighty knows best.
Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (Makruh) for a person in a state of minor ritual impurity (Hadath Asghar) to perform the Adhan. However, if he does so, his Adhan is considered valid and fulfills the sunnah of the Adhan despite it being disliked. And Allah the Exalted knows best.
Is it a condition for the mosque where I‘tikaf is performed to hold Jumu‘ah prayers?
No, it is not a condition for the mosque where I‘tikaf is performed to have Jumu‘ah prayers. However, if a person vows to perform continuous I‘tikaf, and Jumu‘ah occurs within that period, then they must observe I‘tikaf in a mosque where Jumu‘ah is held so that they do not break their continuity by leaving for Friday prayer.
Is a person who forgot to make up missed fasts until the next Ramadan began required to pay expiatory compensation (Fidyah) alongside the makeup fast (Qada')?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Whoever forgets to make up missed fasts of Ramadan (Qada') until the following Ramadan begins incurs no sin, pursuant to the statement of the Messenger of Allah (peace and blessings be upon him): "Indeed, Allah has pardoned for my nation their mistakes, their forgetfulness, and that which they are coerced into doing." [Narrated by Ibn Majah, and Al-Bayhaqi in Al-Sunan Al-Kubra]
Furthermore, such an individual is not obligated to pay a expiatory compensation (Fidyah). It is stated in Bushra Al-Karim (p. 580)—one of the authoritative Shafi'i jurisprudential texts: "As for delaying it [the makeup fasts] due to a valid excuse—such as travel, breastfeeding, forgetfulness, or ignorance of the prohibition of delay (even for one living among scholars)—no Fidyah is required. This is because delaying performance during the actual month is permissible due to these excuses; hence, delaying makeup fasts is even more permissible, even if it continues for years."
And Allah Almighty knows best.