Does passing wind from the anus affect ritual purity?
Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.
What is the ruling on a woman shaking hands with the brothers of her husband`s father, and not putting on Islamic wear before them?
The aforesaid are strangers to the their brother`s son`s wife, therefore, it is forbidden for her to take off her Islamic wear before them, or to shake hands with them.
What is the ruling of Sharia on looking at one`s Mahram women?
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.
A Mahram man (man impermissible for a woman to marry) is permitted to look at what usually appears from his Mahram women (women impermissible for a man to marry) while doing their daily housework, with the exception of their private parts. And Allah The Almighty Knows Best.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.