After watching Martyrs (2008), I kept on thinking about the motive or the message behind that movie. My question is, why was the skin peeled off the entire body of that girl, and what did she tell to the old woman which led the woman to commit suicide?
In Martyr, Mademoiselle was the head of secret philosophical society seeking to discover the secrets of the afterlife through the creation of "martyrs". Their experiments inflict systematic acts of torture upon young women in the belief that their suffering will result in a transcendental insight into the world beyond this one. It include that peeling of the skin etc.
For you second question why Mademoiselle commit suicide?
Answer is in the last lines of Mademoiselle
Mademoiselle: Keep doubting. IMDb
They kept it ambiguous intentionally. There are various theories on reddit about it but they are just plain speculation form the side of viewer.