What is the ruling on taking the answer to an exam question from the teacher after she has asked the students, and is there sin in not informing the supervisor about the teacher? And what is the ruling on sitting with a class that commits evil and not informing the supervisor about them?

There is no blame upon you for benefiting from the answer you received without searching or asking, and you are not obligated to report the teacher unless her actions are repeatedly causing harm. Rather, it is better to conceal her faults. As for those who commit evil deeds, you should advise them first. If they do not respond and persist in their open transgression, then report them to the supervisor and do not sit with them, for Allah Almighty says: "And it has already come down to you in the Book that when you hear the verses of Allah disbelieved in and ridiculed, then do not sit with them until they enter into another conversation. Indeed, in that case, you would be like them."