Is it permissible for a Muslim who holds American citizenship to receive the monthly aid provided by the government, given that his father considers it unlawful wealth due to usurious dealings in America, and is it permissible to take it for charity if it is not permissible to benefit from it personally?

There is no objection to benefiting from government aid for those who are eligible, and no attention should be paid to the fact that some of the state's money is acquired through unlawful means, as much of its money is acquired through other means. This is similar to the case of a person whose wealth is mixed. Scholars have explicitly stated the permissibility of accepting gifts from someone whose wealth is mixed and dealing with them. The Prophet, peace and blessings be upon him, used to accept gifts from kings and engage in trade with Jewish merchants and other polytheists, even though their wealth was mixed with both lawful and unlawful earnings.