What is the ruling on money taken from a school that asks me to claim I am American, even though I am not, knowing that I am a student in China, my English is good, and I complete all my assignments?

It is not permissible to lie by stating something contrary to the truth, for it involves deception and fraud, as Allah Almighty says: "And shun false statement." There is no obedience to a creature in disobedience to the Creator. As for the salary, there is no harm in benefiting from it as long as the work is performed as required, unless the salary differs based on nationality, in which case the increase given due to a false nationality becomes impermissible.