Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
What is the waiting period ('Iddah) for a woman whose husband has passed away, and what is the ruling on her wearing gold?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The waiting period ('Iddah) for a woman whose husband has passed away is four months and ten days for one who is not pregnant. As for a pregnant woman, her waiting period lasts until she gives birth. It is obligatory for her to remain in the marital home, only leaving for a necessity. During this time, it is prohibited (Haram) to display any form of adornment on the body or clothing; this includes wearing kohl, gold, all types of perfume, and dyeing the hair. Likewise, it is prohibited to receive a direct marriage proposal or to marry during this period.
It was narrated by Umm 'Atiyyah that the Prophet ﷺ said: 'We were forbidden to mourn for a deceased person for more than three days, except for a husband, for whom the mourning period is four months and ten days. During this time, we were not to use kohl, nor wear perfume, nor wear dyed clothing except for garments made of 'Asb (coarsely dyed yarn). We were, however, granted a concession at the time of purification—when one of us bathed following her menses—to use a small amount of Kust (costus) or Azfar (fragrant substances). We were also forbidden from following funeral processions.' (Narrated by Al-Bukhari). And Allah the Exalted knows best."
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.
Why was the exact date of Laylat al-Qadr concealed?
The wisdom behind this is to encourage Muslims to strive in worship throughout all the nights of Ramadan, or at least in the last ten nights. By doing so, they will earn the reward of observing Laylat al-Qadr as well as the reward of worshiping on other blessed nights.