Is it permissible for a brother who manages the affairs of his poor mother and sisters, and receives their father's monthly salary, to take something from this money for himself, or to take a fare for transporting them by car to attend to their needs?

If the money is a grant from the state to the deceased's wife and his minor daughters, then it belongs to them, and no one else has the right to take it. However, if it represents entitlements due to the deceased from his employer, then it is a right for all heirs and is to be divided among them according to Islamic law.

If the sisters are adult and of sound mind, there is no objection to agreeing with them on a fee for managing their money. However, if they are minors below the age of maturity, their money may not be managed except by their guardian. If you are the guardian, it is permissible for you to take from their money in a reasonable amount commensurate with your efforts, provided you are in need, in accordance with the Almighty's saying: "And whoever is rich, let him abstain; and whoever is poor, let him eat with honor."

It is permissible to take a fee for transporting the sisters from their money, provided they consent and are aware of the amount of the fee. It is advised that you be a helper to them, not a burden, especially if they are in need.

As for the mother, you should not take anything from her money in exchange for serving her. If you need something from her money, ask her.