How is the beginning of Ramadan determined?
1. Completing 30 days of Sha‘ban, or
2. Sighting the crescent moon after sunset on the 29th day of Sha‘ban.
It is Sunnah to search for the moon, and it is obligatory to follow the official authorities responsible for announcing it.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.
Does collecting saliva and swallowing it break the fast?
Swallowing collected saliva does not break the fast, but it is an unnecessary and meaningless act.