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.
Who should pay the Zakah (obligatory charity) from the orphan`s money?
His/her guardian, and if the latter fails to do so, then the orphan himself/herself is obliged to pay the Zakah once he/she reaches puberty, and is capable of handling his/her own affairs. And Allah Knows Best.
What is the ruling on sacrificing a hornless sheep?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is valid to sacrifice a hornless sheep (al-Jamma’ or al-Jalha’). Similarly, a sheep with a broken horn is also acceptable; it does not affect the validity of the sacrifice even if the break causes bleeding, unless the injury is so severe that it leads to the spoilage of the meat. And Allah the Almighty knows best.
What is the due amount of food in expiation for perjury?
It is feeding ten indigent persons: 600 grams (for each) of the average food of your families such as rice, and it is permissible, according to Imam Ahmad Bin Hanbal, to give that amount in money if it was more useful to them.