What is the ruling on teachers solving exams and periodic assignments and preparing reports for their students in the e-learning system, and does that fall under the suspicion of something unlawful?

Prohibiting cheating in exams and other matters is a fundamental principle, and "whoever cheats is not of us." Cheating in final exams is a deception against the state and Muslims, because it produces weak students who then undertake tasks for which they are not qualified. As for completing assignments and short quizzes, that is a deception against parents and educational oversight bodies. This is considered cheating and a major sin.