When does the time of Isha' prayer end?
All perfect praise be to Allah,The Lord of The Worlds It ends at the emergence of true Fajr (Fajr Al-Sadiq ), and when the second Athaan of Fajr starts.And Allah Knows Best.
Does the intention (niyyah) of the principal (muwakkil) suffice for the sacrifice (dhabḥ) of the udhiyyah?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person appoints an agent (wakīl) to perform the slaughter (dhabḥ) on their behalf, the intention (niyyah) of the principal (the one appointing the agent) suffices, and there is no need for the agent to have this intention himself. In fact, even if the agent is unaware that he is performing the sacrifice on someone's behalf as an udhiyyah (sacrificial offering), this does not affect its validity. And Allah, the Most High, knows best.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.