Is it permissible for a student to change his answer on an exam based on an answer he overheard from a classmate, and what is the ruling on neighboring students knowing his answers without his intention?

If you hear the answer to an exam question unintentionally, there is no blame on you for writing that answer, and it is not considered prohibited cheating. Similarly, if some students look at your answer sheet without your intention and copy something from it, there is no sin upon you. Rather, the sin is upon them if they intended to do so.