Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Can a woman leading other women in Tarawih prayer recite aloud?
Yes, a woman leading other women in Tarawih prayer is allowed to recite aloud, as long as no non-mahram (other than unmarriageable kin) men can hear her.
What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?
Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.
If someone fasts on the White Days with the intention of making up for missed fasts (qada), will they receive the reward for both voluntary and obligatory fasting?
Making up missed obligatory fasts (qada) is mandatory, and the intention for qada must be specified.
If a person makes up their missed Ramadan fasts on the White Days, they must intend qada, but they may also intend to fast the White Days, and Allah willing, they will receive the reward for both.
This is similar to entering a mosque and praying an obligatory prayer, where the person also earns the reward of Tahiyyat al-Masjid (greeting the mosque) if they intend both.
● If the person missed their fasts due to a valid excuse, they may wait and fast on the White Days.
● However, if they missed the fasts without a valid excuse, they must make up the fasts immediately and should not delay them until the White Days.
