What are the rulings of Sharia concerning a brother who killed his brother in self-defense, and are his grandchildren entitled to claim their grandparents' inheritance or return to their original homes?

Taking a life is one of the gravest sins. If the killing is in self-defense, then killing is permissible if the aggressor could not be repelled otherwise. However, if the aggressor could have been repelled without killing, such as by striking or wounding, then killing is forbidden. The killer does not inherit from the slain if the killing was unlawful. As for the killer's children, they have no relation to the killing and are not prevented from inheriting. If it is proven that the killer could have defended himself without resorting to killing, then he is a willful murderer, and subject to Qisas (retaliation) or Diyah (blood money) from his own wealth, unless the heirs of the slain pardon him.