Does buying meat equivalent to the weight of a slaughtered animal and distributing it avail for an udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
That does not avail for the sacrifice (uḍḥiyyah), because the sacrifice necessarily requires slaughtering an animal from the category of anʿām (camels, cattle, and sheep/goats) within a specified time.
Rather, that is considered a form of charity (ṣadaqah) for which one is rewarded. And Allah Almighty knows best.
What is the ruling on the ablution of one who touches women prohibited to him by a temporary prohibition (mahram bi-hurma mu'aqqata)?
It is prohibited to touch a woman who is temporarily prohibited (meaning one whom it becomes permissible to marry after the impediment is removed, such as the wife of a brother or paternal uncle). Touching her without a barrier invalidates ablution. And Allah the Almighty knows best.
What are the key differences between the 'aqīqah and the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The following are the key differences between the 'aqīqah and the uḍḥiyyah:
First: The 'aqīqah is slaughtered as an act of drawing closer to Allah the Almighty and expressing gratitude for the blessing of a newborn child. The uḍḥiyyah, on the other hand, is slaughtered as an act of drawing closer to Allah and expressing gratitude to Him specifically during the days of slaughter (ayyām al-naḥr).
Second: The 'aqīqah is performed on the seventh day from the birth of the newborn, whereas the uḍḥiyyah is performed on Eid al-Aḍḥā and its time extends for three days after the Eid.
Third: The 'aqīqah is performed once in a lifetime for the newborn, whereas the uḍḥiyyah is recommended every year.
Fourth: It is Sunnah for the one intending to offer the uḍḥiyyah to refrain from cutting his hair and nails until after he has slaughtered. This is not a Sunnah for the one intending to perform the 'aqīqah.
Fifth: It is Sunnah for the 'aqīqah to be cooked and distributed to the poor in its cooked form. The uḍḥiyyah, by contrast, must be distributed as raw meat. And Allah Almighty knows best.
What is required of a traveler or a sick person if they broke their fast and then their excuse ceased?
If a traveler settles or a sick person recovers after having broken their fast, it is recommended for them to refrain from eating and drinking for the rest of the day, but it is not obligatory.