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.
What is the meaning of the word aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah in its linguistic sense refers to the hair upon the head of a newborn at the time of birth.
In its Sharī'ah sense, it refers to the livestock that is slaughtered on behalf of a newborn child.
And Allah Almighty knows best.
What is the ruling on purchasing sacrificial animals and authorizing their slaughter via telephone?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is preferable for the one offering a sacrifice (udhiyah) to slaughter the animal himself, in adherence to the Sunnah, or to be present at the slaughter if possible.
It is valid to authorize a butcher to purchase a sacrificial animal on his behalf and slaughter it, regardless of whether the animal is owned by the butcher or the butcher is acting as an agent in its sale—according to the Hanbali school—provided that the butcher specifically designates and purchases the animal for the person offering the sacrifice before slaughtering it. And Allah Almighty knows best.