Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
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 is the ruling on selling sacrificial animals (udhiyah) described with specific attributes and authorizing an agent to slaughter them?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Selling sacrificial animals (udhiyah) that are described with specific attributes is permissible. This falls under the category of a salam sale (forward sale) if conducted using the terminology of salam, and under the category of a regular sale if not using the terminology of salam.
As for authorizing the seller to slaughter the sacrificial animal, the basic principle is that it is permissible, because the agent (wakil) stands in the place of the principal (muwakkil) in achieving his objective. This is a contract that the principal (the buyer) is entitled to perform himself, so authorizing another (the seller) to do so on his behalf is valid.
However, it is a condition for authorization to slaughter that the intention (niyyah) is present either at the time of slaughter or at the time of handing over the sacrificial animal to the agent. The basic principle is that the sacrificial animal must be specifically designated, as it is an act of worship. It is not required to designate it at the time of slaughter; rather, it is valid to do so before that.
It is permissible for the principal either to delegate the intention to the agent or to formulate it himself when authorizing the agent to slaughter. However, the sacrificial animal must be designated, even if at the time of slaughter, by the agent.
It is obligatory to designate the sacrificial animals so that each person offering a sacrifice receives his own specific animal. Therefore, charitable organizations and companies must take this into consideration and establish a specific mechanism that ensures no mixing of sacrificial animals occurs, so that each person offering a sacrifice receives his own designated animal. And Allah Almighty knows best.
What is the Islamic ruling on one who was unable to fast and then regained the ability?
He is not required to make up the fast (Qada) even if he becomes capable of it; whether he regained the ability to fast after paying the fidya (feeding a needy person for each day of missed fasting) or before it, because he was liable for paying it in the first place, so it remains binding upon him. However, if he delayed paying it beyond the first year, nothing is required of him due to the delay. If he is unable to pay it, it does not remain as a debt upon him. And Allah the Exalted knows best.