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 someone who is uncertain whether he omitted one of the ab‘āḍ of the prayer, such as being uncertain whether he omitted the first tashahhud?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The ab‘āḍ include the middle tashahhud and the qunūt in Fajr prayer — for which sujūd as-sahw (the prostration of forgetfulness) is prescribed if left out. Whoever is uncertain, during the prayer, whether he omitted one of these elements, should proceed on the assumption that he did not perform it, and should perform sujūd as-sahw accordingly.
It is stated in ‘Umdat as-Sālik (p. 63): "If he is uncertain... whether he omitted a specific ab‘āḍ element, or whether he performed sujūd as-sahw, or whether he prayed three or four rak‘ahs — he proceeds on the assumption that he did not do it, and performs sujūd as-sahw."
The original principle (al-aṣl) for someone uncertain about [having performed] the first tashahhud is that he assumes he did not perform it. And Allah, the Exalted, knows best.
Does vomiting during the day in Ramadan break the fast?
Intentional vomiting is one of the nullifiers of fasting; whoever vomits deliberately breaks their fast.
However, if vomiting occurs involuntarily, the fast remains valid as long as nothing returns to the body cavity (jauf). If anything is swallowed back, the fast is invalidated.
The Prophet ﷺ said: "Whoever is overcome by vomiting does not have to make up the fast, but whoever induces vomiting deliberately must make it up." [Narrated by Abu Dawood and At-Tirmidhi]
Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.