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.
What is the ruling on sending blessings and peace upon the prophet (PBUH) after the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is a Sunnah to send blessings and peace (As-Salat wa al-Salam) upon the Prophet ﷺ after the Adhan and the Iqamah, for both the caller (Mu’adhin) and the listener. It is permissible to do so aloud after the conclusion of the Adhan. However, it is preferable to maintain a brief pause between the words of the Adhan and the prayers upon the Prophet ﷺ, so that people do not mistakenly assume that sending blessings upon him is an integral part of the Adhan itself. And Allah the Exalted knows best.
Can an Udhiyah be made up if its time is missed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the sacrificial animal (udhiyah) is a voluntary (nafl) offering and its prescribed time is missed after the three days of Tashriq have ended, then it is not to be made up as a sacrifice; rather, it becomes merely a sheep for meat.
However, if it was a vowed (nadhr) sacrifice and its time is missed, then it must still be slaughtered, and the slaughtered animal is to be treated as it would have been during its prescribed lawful time. And Allah Almighty knows best.
Does using a gargling medicine break the fast?
If the medicine reaches the body cavity (jauf), the fast is invalidated. However, if it does not enter the body cavity, the fast remains valid.
Therefore, it is advisable to avoid using it during the day in Ramadan.