Is it permissible to combine Zuhr and Asr prayers for being occupied with a wedding ceremony?
No, it isn`t permissible to combine Zuhr and Asr, or Maghrib and Isha because of being busy with a wedding since the exemption for combining prayers is based on lawful excuses, and this isn`t one of them. And Allah Knows Best.
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 valid to perform Tarawih prayer at home?
It is Sunnah for a Muslim to perform Tarawih prayer in congregation at the mosque.
However, if a person sometimes prays it at home in congregation with their family for a valid reason, there is no harm in doing so.
Should a person who doesn’t offer Tasbeehb (saying Subhaana Rabbiya Al-‘Atheem during Rukoo`, and saying Subhaana Rabbiya Al-A‘laa during Sujood) during Rukoo` and Sujood perform As-Sahw Sujood (prostration of forgetfulness)?
He/ she doesn`t have to perform Sujood As-Sahw, whether he/she didn`t offer Tasbeeh during Rukoo` and Sujood either intentionally ,or unintentionally, provided that the attentiveness of the heart wasn`t undermined since it is a pillar in both.