Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Do ear and nose drops break the fast?
Yes, ear and nose drops break the fast because both the nose and ears are open passages to the body cavity.
How many rak‘ahs are there in Tarawih prayer?
The most complete form of Tarawih prayer consists of twenty rak‘ahs, excluding Shaf‘ and Witr. This is the opinion of the majority of scholars, both past and present, and it is the practiced tradition in the two Holy Mosques.
However, Tarawih is valid with any even number of rak‘ahs, even two rak‘ahs, as long as it is performed with the intention of Qiyam al-Ramadan.
Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.