Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
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.
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.
Is it Permissible to lighten the eyebrows (I.e. Dye them blond)?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Lightening the eyebrows is applying dye to them, and it is permissible to dye hair with other than black. The proof of this is the Hadith related by Muslim on the authority of Jabir told that when Abu Quhafa (Abu Bakr’s father) was brought on the day of the Conquest of Mecca with his head and beard white like hyssop, the Prophet (PBUH) said: "Change this with something, but avoid black."
However, it isn`t permissible for a Muslim woman to show her ornament (Zeenah) in the presence of non-Mahram men (Men permissible for a woman to marry). And Allah The Almighty Knows Best.