Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
What is the Ruling on Reciting the Prophetic Narration?
All Perfect Praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
Reciting the Prophetic narration is permissible as many scholars used to, since in principle, the rulings of recitation have to be observed while speaking Arabic language. And Allah Knows Best.
If the imam does not leave time for reciting Surah Al-Fatihah, is the recitation of Al-Fatihah waived for the follower?
The recitation of Al-Fatihah is not waived for the follower. They should recite it silently, even if it causes a slight delay in following the imam in bowing (Ruku'). And Allah Knows Best.
How many Rak`ahs (unit of prayer) are offered in Witr prayer?
All perfect praise be to Allah, The Lord of The Worlds Witr (an odd number prayer performed between Isha`a and Fajr) is offered with a minimum of one Rak`ah, and a maximum of eleven, but offering three Rak`ahs is the minimum of its complete form. And Allah Knows Best.