What should we do about a brother who practices masturbation everywhere, knowing that he is mentally and visually impaired and does not respond to advice or physical discipline? And what is the religious ruling on leaving him to practice it?

Masturbation is forbidden, and this is the view of most scholars. If one masturbates with his hand but does not ejaculate, he has committed a forbidden act, but it does not invalidate the fast. If your brother is not of sound mind, there is no sin upon him. However, he must be prevented from this objectionable act to the best of one's ability. An objectionable act (munkar) is any deed whose occurrence is prohibited by religious law, and it is more general than a sin. A child and an insane person must be prevented from it. So, if your brother does that while he is awake, scold him to stop. If he does it while he is asleep, overlook it. It is also advisable to refrain from hitting him as long as he is not rational and will not be deterred by it. He can be dressed in trousers that are difficult to open, especially outside the home. A psychiatrist should be consulted to learn the best way to deal with him and help him avoid this forbidden habit.