After a month and a half from the end of postpartum bleeding, my wife occasionally finds a small amount of blood, and she is breastfeeding. What is this blood, and should she fast and pray when she experiences it?
This is postpartum bleeding, so she should not fast or pray until she sees the signs of purity, unless it exceeds sixty days, as the maximum duration for postpartum bleeding is sixty days, and the majority of women experience forty days. If it exceeds sixty days, it is considered irregular bleeding (Istihada). It would be advisable to consult a doctor after the sixty days. And Allah Knows Best.
Is it permissible for someone who has forgotten to mention the supplication pertaining to answering the call of nature to say it while in the toilet?
It is disliked for a Muslim to mention Allah while in the toilet, but he/she may recall the supplication in his/her head without uttering it; that is in case he/she had forgotten mentioning it before entering the toilet.
What is the ruling of Sharia on exfoliating the skin on the face?
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.
According to medical doctors, exfoliation means removing a layer of skin to expose new skin. If this procedure is harmless then it is permissible since this is a kind of treatment and not skinning. 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.