Is an animal that results from crossbreeding between two types of livestock (an'ām) valid [for sacrifice]?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
An animal that results from crossbreeding between two types of livestock (an'ām) is valid [for sacrifice], with consideration given to the higher of the two required ages. Thus, in the case of an animal crossbred between sheep (ḍa'n) and goats (ma'z), only one that has reached two years of age is valid [for sacrifice]. And Allah, the Most High, knows best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
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.
What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.