Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the age of the Aqiqa or the Udhiyah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The minimum age for a sacrificial animal (Udhiyah) and the birth sacrifice (Aqiqa) is as follows:
Camels: Five years old, entering their sixth year.
Cattle and Goats: Two years old, entering their third year.
Sheep: One year old, entering their second year; however, it is permissible for a sheep to be six months old provided it is large in size and plump.
And Allah the Exalted knows best.
Is it a condition for I‘tikaf to be performed in the mosque?
Yes, for I‘tikaf to be valid, it must be performed in a mosque. I‘tikaf is not valid if performed at home or elsewhere.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.