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, but not an udhiyah. And Allah Almighty knows best.
How to pay Zakah (obligatory charity) due on articles of merchandise?
Articles of merchandise are estimated by their whole sale market price at the end of each lunar year, and (2.5%) of their value is paid as Zakah whether it (value) went up, or down compared to actual purchasing price, and whether the increase (profit) was in the article itself such as an increase in the animal`s weight, or in the prices themselves. And Allah Knows Best.
What is the ruling of Islamic Law on a menstruating woman (ḥā'iḍ) reciting the Islamic ruqyah (Qur'anic/spiritual healing)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is permissible for a person in a state of janābah (major ritual impurity), or a menstruating woman (ḥā'iḍ), or a woman in postpartum bleeding (nufasā'), to recite for the purpose of ruqyah (spiritual/Qur'anic healing), even if this includes some verses of the Noble Qur'an — whether recited from memory or by looking at the Muṣ-ḥaf (the physical copy of the Qur'an) without touching or carrying it — provided that the intention behind the recitation is ruqyah, protection (taḥṣīn), and remembrance (dhikr), not the intention of tilāwah (Qur'anic recitation as an act of worship in itself). This remains permissible even if what is recited is an entire sūrah, such as Sūrat al-Mulk.
Imam al-Khaṭīb ash-Shirbīnī (raḥimahullāh) said: "It is lawful for a person in janābah to utter its [the Qur'an's] remembrances and other content — such as its admonitions, its narratives, and its rulings — so long as it is not with the intention of [reciting] Qur'an. [This is] like his saying upon mounting [a vehicle]: 'Glory be to Him Who has subjected this to us, and we could never have accomplished this [by ourselves]' [Sūrat az-Zukhruf: 13] — meaning, [could never have] been capable of it — or upon a calamity: 'Indeed we belong to Allah, and indeed to Him we shall return'... In fact, my teacher, ash-Shihāb ar-Ramlī, issued a fatwā that even if he recited the entire Qur'an without the intention of [reciting] Qur'an, it would be permissible." [Summarized from Mughnī al-Muḥtāj, Vol. 1/P.217] And Allah, the Exalted, 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.