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.
Is it required for a discerning child to make the intention at night if they wish to fast?
If a discerning child wishes to fast during Ramadan, they must make the intention at night because intention is one of the pillars of fasting, even though fasting is not obligatory for them.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
What is the ruling on brown discharge before the menstrual period? Is it considered part of menstruation (Hayd)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Dusky discharge (Kudrah), reddish discharge (Humrah), and yellowish discharge (Sufrah) are all considered menstruation (Hayd) if they occur during the time of the menstrual cycle. If their duration exceeds a day and a night, and the period persists from the first sight of the discharge until the cessation of the menstrual blood—provided the total duration does not exceed fifteen days—then all of it is menstruation. However, if the duration exceeds fifteen days, then the discharge is not considered menstruation, but rather chronic irregular bleeding (Istihadah). And Allah the Exalted knows best.