Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
What is the authenticity of the supplication: "O Allah, bring it upon us with blessings and faith, safety and Islam, and success in what You love and are pleased with. My Lord and your Lord is Allah"?
On the authority of Talhah Ibn Ubayd Allah (may Allah be pleased with him) who reported that the Prophet (PBUH) would say when he saw the crescent moon: "O Allah, let this moon appear over us with blessings and faith, safety and Islam. My Lord and your Lord is Allah."
This was narrated by Tirmidhi (Hadith no. 3451), who said: "It is a Hasan (good) Hadith."
And Allah The Almighty Knows Best.
What is the ruling on the mother who resorts to practitioners of witchcraft to make her son hate his wife?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
What she is doing is forbidden and amongst the seven destructive sins. Hence, she must make repentance, seek forgiveness from Allah, regret what she has done and adhere to the teachings of Sharia. And Allah The Almighty Knows Best..
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.