Is working in a center for correcting exam papers that include questions about the beliefs and practices of various religions considered aiding in sin and spreading false religions? Is the money earned from this work unlawful (haram)? And is the body that grew from this money considered ill-gotten (suht)?

The work is permissible because its nature (collecting, entering, or printing grades) is permissible, and the materials it deals with (such as mathematics, physics, and languages) are also permissible. The only issue lies with the "Religious Studies" material, which contains violations of Islamic law or distortions of Islam. However, since the nature of your work is limited to collecting and printing grades without teaching or correcting, it is not considered direct assistance in sin. There remains a kind of doubt in the matter, though it does not reach the level of prohibition. You can continue with the work while trying to avoid participation in papers related to religious studies, based on the saying of the Prophet, peace and blessings be upon him: "Leave what makes you doubt for what does not make you doubt."