Is money earned lawful if the country's law permits actions that are essentially deceitful and fraudulent, such as receiving student aid designated for academic tasks?

The system mentioned does not appear to involve anything that falls under the category of cheating. Cheating occurs when one violates the system's conditions or defrauds the law. It is not recommended for a Muslim to seek aid if he is not in need, lest his hand be the lower one, especially if the upper hand belongs to a disbeliever. Seeking aid is prohibited if it will lead to committing something forbidden, such as lying or cheating, or if it leads to a trial concerning one's religion or self. It is permissible to accept aid from a disbelieving state if it does not result in abandoning an obligation or committing a forbidden act, and it must be taken through official channels without lying.