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 a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
What do you say about someone who stays up all night on Laylat al-Qadr but misses Fajr prayer?
Such a person has deprived themselves of a great reward. Performing obligatory acts is more beloved to Allah than voluntary acts. Fajr prayer is an obligation, and performing it in congregation is equivalent to worshiping for the entire night. So how can someone neglect it while striving for voluntary prayers?!
What is the ruling on the white discharge (*Al-Qassat al-Bayda'*) if it is in a very small amount—is it considered a sign of purity?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Among the signs of purity (Tahr) for a woman is the white discharge (Al-Qassat al-Bayda'), which is a clear, pure white fluid, regardless of whether it is minimal in quantity, or complete dryness (Jafaf), wherein secretions cease entirely such that if a white cotton cloth is inserted, it comes out completely clean. Once a woman observes either of these two signs, she has attained ritual purity.
Furthermore, another sign of purity is when the duration of the menstrual period exceeds the maximum limit of menstruation, which is fifteen days. If it exceeds this period, it becomes evident that she is experiencing non-menstrual bleeding (Istihadah).