Is remaining in classrooms that involve an explanation of false beliefs—while the heart denies them—considered apostasy? And what should I do about it, and how should I answer in exams?

There is no harm in studying literature books that contain things contrary to creed, and attending what contains disbelief with heart's disapproval and discontent, and disbelief does not occur thereby. There is no harm in answering during an exam with the information you have studied, as long as you do not believe in its meaning.