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.
Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the miscarried embryo.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
One day, I swore that my wife will be unlawful to me to quit smoking hookah?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
The best course of action is that you turn to Allah for help and quit the hookah. In addition, acquainting yourself with the risks of smoking hookah will help you take this step. And Allah, The Most Exalted Knows Best