Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.
What is the ruling on speaking while relieving oneself?
It is disliked for one relieving himself to speak while doing so, except out of necessity. And Allah the Almighty 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.