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.
What is the ruling if a postpartum woman becomes pure before forty days; are acts of worship obligatory upon her, and is she permissible for her husband?
If the postpartum woman becomes definitely pure before forty days, she must perform the ritual bath and perform acts of worship as a pure woman does. What was prohibited for her also becomes permissible, so she becomes permissible for her husband after her bath. The minimum duration for postpartum bleeding is a moment (an instant), and its usual maximum is forty days. Reaching forty days is not a condition; rather, it is sufficient for the blood to stop or to see the white discharge (qassa bayda'). And Allah the Almighty knows best.
Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.
What is the ruling on using a miswak (tooth-stick) during the day in Ramadan?
It is permissible to use a miswak before noon while fasting. However, according to the Shafi'i school, it is disliked (makruh) after noon in order to preserve the natural effect of fasting in the mouth, as the Prophetﷺ said in authentic hadith:
"The breath of a fasting person is more pleasant to Allah than the fragrance of musk."