Is the one who pays his father's internet bill sinful if his brother uses the internet for unlawful purposes with the family's permission, and is it considered disbelief if he allows his brother to play games that contradict the creed on his computer?

If you know that your brother is using the computer for impermissible things, it is not permissible for you to enable him to do so, because that falls under cooperating in sin and aggression, and you would become a partner with him in it. For Allah, the Almighty, said: "And do not cooperate in sin and aggression." A Muslim must be a helper to his brothers in righteousness and piety, not in disobedience. If it is highly probable that the borrower will use the device for impermissible acts, then lending it becomes forbidden and invalid. You must advise him and warn him of Allah, and emphasize that he should not use the device except in what pleases Allah, remembering the saying of the Prophet, peace and blessings be upon him: "Whoever seeks Allah's pleasure by the displeasure of people, Allah will suffice him against the people. And whoever seeks the pleasure of people by Allah's displeasure, Allah will entrust him to the people."