What is the ruling regarding this child in terms of foster-brotherhood with the sons and daughters who nursed from the same mother, and what are his rights over them and the homes in the future?

We congratulate the questioner on sponsoring an orphan due to the immense reward it entails, for the Prophet, peace and blessings be upon him, said: "I and the sponsor of an orphan will be in Paradise like this," and he gestured with his index and middle fingers, slightly separating them. If the wife has nursed the orphan, he becomes their son by suckling and a brother to all their children. As for sponsoring an orphan, it is a voluntary act, and no obligatory rights devolve upon the sponsor or their children after the orphan reaches maturity. The full reward for sponsoring an orphan is attained when he no longer needs sponsorship.