Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.
What is the ruling on making up the regular *rawātib* (sunnah) prayers together with a missed obligatory prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to make up (qaḍāʾ) a missed obligatory prayer (farḍ). As for the timed supererogatory prayers (al-sunan al-muʾaqqatah) or the regular rawātib prayers, it is recommended (mandūb) to make them up, even if a long time has passed. Ibn Ḥajar (may Allah have mercy on him) said in his Fatāwā: "It is established in our school that it is sunnah to make up the timed voluntary prayers, by night or by day, even if congregation is not prescribed for them, whether much time has passed or little."
Accordingly, it is recommended to make up the sunan together with the obligatory prayer. And Allah Almighty knows best.
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Note on terminology: Al-nawāfil al-muʾaqqatah (timed voluntary prayers) refers to supererogatory prayers tied to a specific time or cause, such as the rawātib (regular prayers before and after the obligatory ones), Duha, and the like. The ruling given here reflects the Shāfiʿī position.
What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
