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.
What is the ruling on using a miswak (tooth-stick) during the day in Ramadan?
It is permissible to use a miswak before noon while fasting. However, according to the Shafi'i school, it is disliked (makruh) after noon in order to preserve the natural effect of fasting in the mouth, as the Prophetﷺ said in authentic hadith:
"The breath of a fasting person is more pleasant to Allah than the fragrance of musk."
What is the virtue of Laylat al-Qadr?
It is enough to know its great status that Allah revealed an entire surah about it—Surah Al-Qadr. Moreover, the Quran was first revealed on this night.
Allah says {what means}:
"We have indeed revealed this (Message) in the Night of Power: And what will explain to thee what the night of power is? The Night of Power is better than a thousand months. Therein come down the angels and the Spirit by Allah's permission, on every errand: Peace!... This until the rise of morn!" [Al-Qadr/1-5]
The Prophet ﷺ taught us to observe I‘tikaf in the last ten nights of Ramadan, seeking Laylat al-Qadr. Whoever worships Allah and revives this night will receive the reward of worshiping for a thousand months—excluding Laylat al-Qadr itself.
Is it permissible for someone who is unable to fast to pay the fidyah (ransom/compensation payment) to himself, due to his own poverty?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is not permissible, nor does it fulfill the obligation, for a sick person who is currently and permanently unable to fast to pay the fidyah (ransom/compensation payment) to himself, since it is a financial obligation owed by him, established as a standing debt upon him — much like any other debt he owes. If he were to pay it to himself, it would not thereby be discharged. So if he cannot find [anyone eligible to] pay it to, it remains a standing obligation upon him, and is not thereby waived. If Allah, the Mighty and Majestic, later grants him wealth, it becomes obligatory upon him to pay it out to the poor and needy.
Imam al-Khaṭīb ash-Shirbīnī (raḥimahullāh) said: "There is no difference in the obligation of the fidyah between the wealthy and the poor person; its benefit lies in its remaining established as a standing debt upon the poor person [until he is able to pay it] — and this is the more correct position (al-aṣaḥḥ), as indicated by the wording of ar-Rawḍah and its source text." [Mughnī al-Muḥtāj, Vol.2/P.174]
Accordingly: it is not permissible for a Muslim to pay the fidyah to himself while he remains poor. If the sick person is poor, he is not obligated to pay the fidyah immediately, and it remains a standing debt upon him until a time when he has sufficient means and wealth. And Allah, the Exalted, knows best.