Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for one who sacrifices on behalf of another with his permission to eat from the sacrifice with his permission, and he takes his place in distributing its meat.
It is stated in Hashiyat al-Jamal 'ala Sharh al-Minhaj (Vol.5/P.262): 'If a person sacrifices on behalf of a living individual with his permission, does he take the place of that individual in distributing the meat, because permission for the sacrifice implies permission for distribution, or does it depend on explicit permission? There is room for consideration, but the former view is not far-fetched.' And Allah Almighty knows best."
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
What is the meaning of the word aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah in its linguistic sense refers to the hair upon the head of a newborn at the time of birth.
In its Sharī'ah sense, it refers to the livestock that is slaughtered on behalf of a newborn child.
And Allah Almighty knows best.
Is it permissible to sacrifice imported livestock (Such as Romanian, Australian, etc.)?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
As long as the sheep meets the prescribed Sharia age and is free from disqualifying defects, it is valid for sacrifice regardless of its country of origin. Therefore, it is permissible to offer sacrifices from various sources, such as: Romanian, Australian, Spanish, Indian, Sudanese, local (Baladi) livestock, and others. And Allah the Almighty knows best.