Is it permissible for the woman to use her mobile phone while on the street?

All Perfect Praise is due to Allah, The Lord of The Worlds 

Modesty should be observed by the woman at all times, so she is free to use her phone while on the street as long as it is done within the limits of Islamic manners. And Allah The Almigty Knows Best.

Is it permissible for a Muslim physician to specialize in GYNECOLOGY OBSTETRICS, and what is the ruling on working as such?

Some fields of knowledge are an individual duty while others are a collective one, and specializing in GYNECOLOGY OBSTETRICS is a collective duty. However, if there were female physicians to treat women, then there is no need for a male GYNECOLOGY OBSTETRICS specialist to look at women`s Awrahs (private parts) except in necessary situations since the jurisprudential maxim says:” Necessity must only be assessed and answered proportionately.”

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 it incumbent on a wife whose husband hasn`t gone to bed with her(for sexual intercourse) for many years to observe `Iddah(waiting period) upon his death?

Upon the death of the husband, a wife is obliged to observe the `Iddah even if he hadn`t slept with her because she inherits him.