Is the money my brother received after two years of working in journalism permissible or forbidden, knowing that he withdraws from it periodically to buy household necessities?

What your brother withdrew from his bank account is lawful for him, because he withdrew from his capital. However, if the bank is usurious and the deposit of money resulted in usurious interest, he is obligated to dispose of it by spending it on the welfare of Muslims and giving it to the poor and needy. It is not permissible to deposit money in usurious banks when an Islamic alternative exists, because that is considered assisting them in their sin.