Is helping one's father fill out internet data considered assisting in sin if one's brothers use it to watch TV series and listen to music, and what should I do if my refusal leads to the father's anger towards the brothers?

There is no blame upon you for helping your father to provide internet service, because it does not involve aiding in disobedience so long as it is primarily used for permissible matters. If your siblings use it for forbidden things, then you must forbid them and explain the legal ruling to them, and threaten them by informing your father. If they do not desist, then inform him so that he may prevent them.