Is it permissible for "S" to take his right from "A"'s money with the father's knowledge, and is giving "S" a power of attorney by the sister considered a breach of trust, and is it permissible for the sister to accept real estate from "S"?

It is not permissible to favor some children over others in gifts except for a legitimate Shar'i reason. Preventing daughters from inheriting is a pre-Islamic custom that Islam abolished. Any of the children has the right to take their due share that Allah has ordained for them, provided that this does not lead to discord or indecency.