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.
Is it permissible for a wife to boycott (not to attend to his different needs) her husband?
It isn`t permissible for the woman to boycott her husband unless he is the reason behind that, and it is recommended that both spouses seek the advice of righteous people to make reconciliation.
What is the ruling on eating or drinking during the second Adhan?
It is not permissible to eat or drink during the second Adhan because it announces the break of dawn and the obligation to start fasting. Allah Almighty says {what means}:"and eat and drink until you can discern the white streak of dawn against the blackness of night." [Al-Baqarah/187].
Whoever eats or drinks during this time invalidates their fast, and they must refrain from eating for the rest of the day and make up for the missed fast later.
If a traveler settles or a sick person recovers while fasting, is it permissible for them to break their fast?
● If a sick person starts the day fasting and then recovers during the day, they must complete their fast.
● If a traveler starts the day fasting and then settles (returns or stops traveling) during the day, they must also complete their fast.
● It is forbidden for both of them to break their fast because the concession (rukhsah) is no longer valid once its reason disappears.