Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
What is the ruling of Sharia on male doctor delivering a baby?
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.
The person most entitled to deliver a baby is a Muslim woman, then a woman from the People of the Book, then a woman from the disbelievers, then a Muslim man, then a man from the People of the Book. However, if there was no woman to deliver the baby, then it is permissible for a male doctor do deliver it. And Allah The Almighty Knows Best.
What is the Islamic ruling on parents asking son to divorce his wife?
Praise be to Allah the Lord of the Worlds.
If their asking him to do so is justified in Sharia, then there is no blame on him to obey them. And Allah The Almighty Knows Best.
Who is obligated to fast?
The one obligated to fast is the Muslim who is of sound mind, mature, capable of fasting, and free from obstacles such as menstruation or postpartum bleeding. And Allah Knows Best.