Is the two Raka's after Friday Prayer an act of Sunna?
Performing Two prostrations after the call of Friday's Athan is an act of Sunna, since Al-Bukhari stated in his Sahih: (The chapter of praying before and after Friday's prayer). This indicates that he mentions Friday's prayer exactly as the Duhr prayer (Afternoon prayer) as regards praying before and after the call of Athan. And Allah Knows Best.
Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.
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.” And Allah Knows Best.