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 are the nullifiers of fasting?
1. Anything that enters the body cavity intentionally, even in small amounts, through an open passage such as the mouth, nose, ears, front, or back private parts.
2. Intentional vomiting.
3. Sexual intercourse.
4. Masturbation.
5. Menstruation and postnatal bleeding.
6. Insanity.
7. Apostasy.
8. Fainting if it lasts for the entire day.
What is the ruling on offering an Udhiyah on behalf of another with their permission?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for a person to offer a sacrifice (Udhiyah) on behalf of someone else with their permission, even if the person performing it has not offered a sacrifice for themselves. It is stated in Sharh Manhaj al-Tullab (Vol.5/P.261) by Zakariya al-Ansari: "No one may offer a sacrifice on behalf of another without their permission... as opposed to when permission has been granted." And Allah the Almighty knows best.
Is Zakah (obligatory charity) due on the money saved for marriage?
Zakah is due on the money saved for marriage if it reached the Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over possessing it.