Is it permissible for a woman to work in America in a way that violates the conditions of her residency visa, which prohibits her from working or studying?

By virtue of his residence in those lands, a Muslim is obliged to respect laws that do not contradict the Sharia, and it is not permissible to violate them because one of the conditions for granting residency is respect for the law. Allah has commanded fulfilling contracts: "O you who have believed, fulfill [all] contracts," and the Prophet, peace and blessings be upon him, said: "Muslims are bound by their stipulations." Based on this, you are not permitted to work as long as you have committed to this condition by obtaining the visa.