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 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.
What are the Sunnahs and etiquettes related to the slaughtering of an animal?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
1-Avoid terrifying the animal before it is slaughtered.
2-Do not slaughter the animal in front of others of its kind.
3-Offer water to the animal before the sacrifice.
4-Sharpen the knife thoroughly prior to slaughtering to ensure the cut is made as quickly and cleanly as possible. This is in accordance with the statement of our Master, the Prophet (peace and blessings be upon him): "Indeed, Allah, the Almighty and Majestic, has prescribed excellence (Ihsan) in all things. So when you kill, kill well; and when you slaughter, slaughter well. Let each of you sharpen his blade, and let him put his sacrificial animal at ease." (Narrated by Muslim)
Do not begin skinning the carcass until you are absolutely certain that the animal has completely passed away.
Slaughter cattle, sheep, and goats while they are lying down on their left side, facing the Qiblah (direction of prayer). Leave the right leg untied so the animal can move it, helping it rest more easily during its final moments. For camels, however, the preferred method (Nahr) is to slaughter them while they are standing up, with their left knee tied. And Allah the Almighty Knows Best.
What is the ruling of Islam on swearing by Allah without intending to take an actual oath?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If someone swears by Allah without intending to take an actual oath, and without the firm resolve to bind themselves to it, then there is no sin or expiation (Kaffarah) required of them. Allah the Exalted says {what means}: 'God will not call you to account for thoughtlessness in your oaths, but for the intention in your hearts; and He is Oft-forgiving, Most Forbearing.' [Al-Baqarah/225]. However, a Muslim should avoid swearing oaths excessively so that their tongue does not become accustomed to it. Allah the Exalted says {what means}: 'And make not God’s (name) an excuse in your oaths against doing good, or acting rightly, or making peace between persons; for God is One Who heareth and knoweth all things.
' [Al-Baqarah/224]. And Allah the Exalted knows best."