Does smoking break the fast?
Yes, smoking breaks the fast because smoke particles intentionally enter the lungs, which are considered part of the body cavity (jauf).
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.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.