Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
Can a woman leading other women in Tarawih prayer recite aloud?
Yes, a woman leading other women in Tarawih prayer is allowed to recite aloud, as long as no non-mahram (other than unmarriageable kin) men can hear her.
What are the legal and religious consequences for a charitable organization in the event that a sacrificial animal is damaged or spoiled after slaughter?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Charitable organizations entrusted with slaughtering sacrificial animals (uḍḥiyyah) and distributing their meat on behalf of their owners are obligated to safeguard the meat from spoilage, damage, theft, and any other harm. This is because such organizations act as agents (wukalā') on behalf of those offering the sacrifice, and an agent holds what is entrusted to them in trust (amānah) — whether they receive a wage for their work or act on a voluntary basis.
If the sacrificial animal is damaged after slaughter during the processes of packaging, transportation, or storage due to negligence or oversight — whether on the part of the organization's own staff overseeing the operation, or on the part of third parties contracted by the organization such as transport or shipping companies — then liability falls upon the negligent party, who is required to compensate for the value of the sacrifice. It is not permissible to cover such compensation from the organization's other donor funds.
However, if the damage to the sacrificial animal occurs without any negligence in its preservation and storage on the part of any party involved in the transportation, shipping, or storage process, and is instead attributable to force majeure circumstances beyond their control, then no financial liability is borne by any party in such a case. And Allah Almighty knows best.
Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
It is permissible for someone who sacrificed on behalf of another with their permission to eat from it with their permission, and they stand in their place (act as their representative) in distributing it.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.8/P.141): "And he—meaning the one sacrificing on his own behalf, provided he has not apostatized—has the right to eat from a voluntary sacrifice and his sacrificial gift; rather, it is recommended. As for an obligatory sacrifice, it is forbidden for him to eat from it, whether it was designated as such initially or as a liability in his dhimmah. And excluded by what has preceded is if he sacrifices on behalf of another, or if he apostatized, then it is not permissible for him to eat from it, just as it is absolutely impermissible to feed a disbeliever from it."(The text I found indicates the impermissibility of eating) ???
And it is stated in Hashiyat al-Jamal ‘ala Sharh al-Manhaj (Vol.5/P.262): "If a person offers a sacrifice on behalf of a living person with their permission, does he act as their representative in distributing it—on the grounds that permission to sacrifice is permission to distribute it—or does it depend on their explicit permission? This requires consideration, but the first view is not far-fetched." And Allah the Almighty knows best.
