Does sacrificing one sheep avail for the entire household?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Offering an Udhiyah (sacrificial offering) is a communal Sunnah (Sunnah Kifayah) for members of the same household, provided that their financial maintenance is undertaken by a single provider. By "communal Sunnah," we mean that when one person performs it, the religious recommendation is fulfilled on behalf of the entire household, though the spiritual reward itself belongs uniquely to the one who offered it.
Therefore, if any member of the household performs the sacrifice—even if it is someone who is not legally responsible for the household's expenses, such as the wife or one of the children—the recommendation is fulfilled for everyone in that home. However, the reward does not automatically extend to the other members unless the person offering the sacrifice explicitly intends to share the reward with them—similar to how performing a funeral prayer (Janazah) fulfills the communal obligation for everyone, yet the specific reward is earned by those who actually prayed.
Additionally, a single sacrifice is sufficient for a man who is married to more than one wife. And Allah the 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.
What is the ruling on combining (jam‘) and shortening (qaṣr) prayers when travel is repeated on a daily basis?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
A traveler is permitted to avail himself of the concessions of shortening and combining prayers once the distance of his journey reaches (81 km) or more. This is on condition that his journey is a permissible one, and that he begins shortening and combining only after setting out and passing beyond the built-up limits of the city in which he resides, or beyond the administrative boundaries of the area where he lives.
Accordingly, if the distance between one's workplace and one's place of residence reaches the distance upon which the concession of combining and shortening depends, then combining and shortening are permissible once he leaves the built-up area, even if this travel is repeated on a daily basis.
Ash-Shirbīnī (raḥimahullāh) said: "It is permissible to combine Ẓuhr and ‘Aṣr, either as an early combination (taqdīm) in the time of the first, or as a delayed combination (ta'khīr) in the time of the second; and likewise Maghrib and ‘Ishā' — either early, in the time of the first, or delayed, in the time of the second — during a long, permissible journey, in following [the Prophet's practice]. As for the delayed combination, it is established in the two Ṣaḥīḥs from the ḥadīth of Anas and Ibn ‘Umar (raḍiyallāhu ‘anhum). As for the early combination, Ibn Ḥibbān and al-Bayhaqī graded it ṣaḥīḥ from the ḥadīth of Mu‘ādh, and at-Tirmidhī graded it ḥasan." [Quoted with slight abridgment from Mughnī al-Muḥtāj, Vol.1/p.529]
The conditions for combining and shortening have already been explained in Fatwa No. 14 and Fatwa No. 842. And Allah, the Exalted, knows best.
What is the ruling on one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?
Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.