What is the ruling of Islamic Law on leaving the Sunnah prayer of Dhuhr due to fatigue?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
According to the general rule, a Muslim should strive to maintain the Sunnah prayers before and after the obligatory prayers (al-sunan al-qabliyyah wa al-ba'diyyah). One is permitted to pray them sitting from the outset, but if one leaves them due to severe fatigue, there is no objection to doing so. It is recommended (mustahabb) to make up (qadā') a time-bound supererogatory prayer (nafl mu'aqqat) at any time if it was missed.
Al-Shirbīnī (may Allah have mercy on him) said: "If a time-bound supererogatory prayer is missed, it is recommended to make it up according to the more authoritative view (al-azhar), based on the hadith recorded in the two Ṣaḥīḥs: 'Whoever sleeps through a prayer or forgets it should pray it when he remembers it.' This is also supported by the fact that the Prophet (peace and blessings be upon him) made up the two rak'ahs of Fajr when he and his companions overslept in the valley and missed the dawn prayer until the sun had risen [narrated by Abū Dāwūd with an authentic chain]." And Allah, the Most High, knows best.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.
What is the ruling on performing ablution (wudu') and ritual bathing (ghusl) with Zamzam water?
It is permissible to perform ablution and ritual bathing with Zamzam water. However, scholars disliked using it for cleaning after relieving oneself (istinja'). And Allah the Almighty knows best.
What is the ruling on giving the expiation of an oath (Kaffarat al-Yamin) to a charity that feeds the poor?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is allowed for a Muslim to appoint a proxy (agent) to distribute the expiation (Kaffarah) on their behalf. Our jurists have explicitly stated the permissibility of delegation (Tawkil) in the distribution of Zakat, Kaffarah, and vows (Nadr).
It is stated in Mughni al-Muhtaj (Vol.3/P.237): 'One has the right to pay the Zakat of their wealth personally... and they also have the right to delegate it.' And Allah the Exalted knows best.