Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible to read from the Mus-haf during Tarawih prayer?
Yes, it is permissible to read from the Mus-haf during Tarawih prayer, provided that excessive movements that invalidate the prayer are avoided.
However, it is preferable for the imam to be a memorizer of the Quran and to recite from memory.
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.
What is the ruling on fasting?
Fasting in Ramadan is an individual obligation (Fard ‘Ayn) upon every mature, sane Muslim who is capable of fasting.
Fasting can also be recommended (Mustahabb), such as voluntary fasting on Mondays and Thursdays, fasting on the Day of Arafah for those not performing Hajj, and fasting on Ashura.
Fasting can be prohibited (Haram), such as fasting on the two Eid days, the Day of Doubt (Yawm al-Shakk), and the Days of Tashreeq.
Some types of fasting are disliked (Makruh), such as singling out Friday or Saturday for fasting without a specific reason and fasting on the Day of Arafah for a pilgrim.