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 can a menstruating woman do on Laylat al-Qadr?

If a menstruating woman engages in remembrance of Allah (dhikr), supplication (du‘a), and sincere devotion, she has indeed observed Laylat al-Qadr. She may also listen to the Quran from audio sources such as the radio or television.

Is it a condition for I‘tikaf to be performed in the mosque?

Yes, for I‘tikaf to be valid, it must be performed in a mosque. I‘tikaf is not valid if performed at home or elsewhere.

Is it permissible for a woman to perform the obligatory prayer immediately after the adhan and before the Iqamah is performed in the mosque?