Is it true that whatever is dry is pure even if there was impurity on it?
The impure material object does not soil (make impure) anything else unless the impurity is wet and transferable. But, if the impurity is dry or non-transferable, then there is no problem. Fuqaha has stated that: There is no disagreement between Muslim scholars that when a dry impurity touches something dry it does not make the latter impure.
Should a pregnant woman who broke fast because of pregnancy make it up, and is a ransom due on her?
The pregnant and the suckling, if they fear for their health, may break their fast and make up for it, and no ransom is due on them. However, if they broke fast in fear for the fetus and the baby, then they are obliged to make up for it, and pay the ransom which is feeding a needy person for each of the missed fasting days. And Allah Knows Best.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
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.