Which takes precedence: the 'aqīqah or the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is an act of worship through which a servant draws closer to Allah the Almighty in gratitude for the blessing of a newborn child. It is a confirmed Sunnah for those who are financially capable, and Allah does not burden any soul beyond what it can bear.
However, the uḍḥiyyah takes precedence, as it is a confirmed Sunnah established from the Prophet ﷺ through stronger and more numerous narrations — indeed, the Ḥanafī scholars hold it to be obligatory. Furthermore, its time is narrow and limited, expiring with the passing of the days of Eid, whereas the 'aqīqah may be delayed until one becomes financially capable of performing it.
And Allah Almighty knows best.
I bought an apartment, and I am saving money to pay the remaining balance of its price — is zakāh obligatory on this money?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on all saved/hoarded wealth. Once the total wealth reaches the niṣāb (minimum threshold liable for zakah— equivalent to the value of 85 grams of pure 24-karat gold) and a full ḥawl (lunar year) has elapsed over it, zakāh becomes obligatory at a rate of (2.5%) — even if the wealth is earmarked for basic future needs, and even if the wealth's owner is in debt. Debt does not prevent the obligation of zakāh, nor is it deducted when calculating the zakāh due, based on the general and unrestricted wording of all the Qur'anic verses commanding zakāh, which draw no distinction between someone in debt and anyone else.
It is stated in ‘Umdat as-Sālik, from the books of the Shāfi‘ī school: "If someone possesses exactly the niṣāb, and owes an equivalent amount in debt, zakāh remains obligatory on what is in his possession, and the debt does not prevent this obligation" — meaning, the obligation of zakāh on what is presently in his possession.
The ḥawl (annual cycle) recognized for zakāh, as well as for the other sharī‘ah obligations that Allah, the Exalted, has imposed upon Muslims, is the Hijrī (lunar) year. And Allah, the Exalted, knows best.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
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.