Can an Udhiyah be made up if its time is missed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the sacrificial animal (udhiyah) is a voluntary (nafl) offering and its prescribed time is missed after the three days of Tashriq have ended, then it is not to be made up as a sacrifice; rather, it becomes merely a sheep for meat.
However, if it was a vowed (nadhr) sacrifice and its time is missed, then it must still be slaughtered, and the slaughtered animal is to be treated as it would have been during its prescribed lawful time. And Allah Almighty knows best.
Are school exams a valid excuse for breaking the fast in Ramadan?
School and university exams are not considered a valid excuse for breaking the fast, as most students take their exams while fasting without experiencing extreme hardship. Fasting does not conflict with exam preparation, and a Muslim seeks strength in obedience to Allah for both worldly and spiritual matters.
What is the ruling on one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?
Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.
What is the ruling on praying seated due to severe obesity, given that I experience hardship in performing the prayer — especially when rising from the ground after sujūd to perform the next rak‘ah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Standing, when one is able to do so, is a pillar of the prayer. However, whoever would experience severe, intolerable hardship, or fears harm to himself or to a limb due to obesity, or finds that standing causes him to lose his khushū‘ (humble focus and concentration) in prayer, then there is no objection to his praying seated on a chair or on the ground, performing rukū‘ (bowing) and sujūd (prostration) through gesture — provided that the gesture for sujūd is made lower than that for rukū‘. Whoever is able, at any point, to properly perform any one of these pillars, is obligated to perform it in full; for omitting it is a concession that applies only in cases of genuine inability. The Prophet ﷺ said: "When I command you to do something, do of it whatever you are able." (Related by al-Bukhārī). As the scholars of fiqh have established: what remains possible is not waived on account of what is difficult.
The criterion for determining genuine inability, as chosen by Imam al-Ḥaramayn al-Juwaynī (raḥimahullāh), is that the worshipper experiences hardship that causes him to lose his khushū‘.
As for voluntary (nafl) prayer, there is no objection to performing it while seated, even if one is able to stand. However, rukū‘ and sujūd must still be performed [in their proper physical form] by anyone who is able to do so. And Allah, the Exalted, knows best.