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.
What is the ruling on the prayer of the individual following the imam whose prayer is broadcasted via television?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Among the conditions for the validity of following an Imam (Sihhat al-Iqtida’) is that the Imam and the follower (Ma’mum) must be in the same location. Therefore, the prayer of one who follows an Imam whose prayer is being broadcast via television from a distant location is not valid. However, if the follower is with the Imam in the same mosque, the prayer is valid. And Allah the Exalted knows best.
Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?
It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.
What is the ruling on someone who prays but does not fast, without a valid excuse?
Fasting is one of the pillars of Islam, and a Muslim's faith is incomplete if they neglect the obligation of fasting while being physically capable of observing it.