Is it obligatory for me to inform the Educational Supervision Center about the study materials that the teacher ordered to keep secret, and if the center does not know about it, am I sinful? And is it obligatory for me to report students whom I suspect of polytheism or any violation of school rules?

You must be careful about declaring Muslims to be disbelievers (takfir), as this is a grave matter with conditions and regulations that only scholars are skilled in. You must be certain that major disbelief (kufr akbar) has occurred and that its conditions are met in the specific individual. The girl might be ignorant, and the verses might not be polytheistic (shirk) as you thought. The fundamental principle is that whoever is confirmed to be a Muslim does not cease to be so except with certainty.

Your duty is to explain the polytheism in the verses and to warn against believing soothsayers, not to declare someone a disbeliever. The Prophet, peace and blessings be upon him, said: "Any man who says to his brother, 'O disbeliever,' one of them will have certainly incurred it."

There is no harm in you taking the exam. If you see a violation of Islamic law, advise first. If the wrongdoing is not removed, seek help from the school administration. Beware of obsessive thoughts (waswas) about declaring your sisters disbelievers. Maintain good relations with your colleagues and do not focus on reporting every transgression you perceive, for you might be mistaken.