A woman became pure [from menstruation] before Fajr, but did not perform ghusl until after sunrise — what is the ruling on her fast?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Her fast is valid, since ghusl (ritual bathing) is not a condition for the validity of the fast, but rather for the validity of the prayer. However, she is sinful for delaying the Fajr prayer beyond its designated time without a valid excuse.
It is known that the time for Fajr prayer ends at sunrise. Nevertheless, she must still perform ghusl, and make up the Fajr prayer. And Allah, the Exalted, knows best.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
Is it valid to have Suhoor before sleeping, even if it is before midnight?
Suhoor refers to the pre-dawn meal eaten after midnight to help a Muslim endure fasting. The closer it is to Fajr, the better.
The Prophet ﷺ said: "My Ummah will remain upon goodness as long as they hasten to break the fast and delay Suhoor." [Narrated by Ahmad]
This is because delaying Suhoor makes it more effective in providing strength for worship. However, if there is a risk of Fajr entering while eating, one should refrain from Suhoor out of caution.
The Prophet ﷺ said: "Leave what makes you doubt for what does not make you doubt." [Narrated by Al-Tirmidhi]
Is the prayer of a woman who is led by an Imam via T.V. permissible?
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. Amongst the conditions for the validity of prayer is that both the Imam and those led by him must be in the same place. Thus, the prayer of the person who is being led by a televised Imam is invalid unless he/she was with him in the same mosque. And Allah Knows Best.