I don't know of any third-party module which offers this type of functionality. It would help to have a couple of example questions you are planning to use.
One possibility would be to use the the normal quiz activity. After the student goes through and completes the quiz, the teacher can "Review" the results and make comments for each question. After the teacher finishes making comments, the student can again review the quiz to see what the teacher added. The downside to using the quiz is that when using multiple choice, one answer is going to have to be set up as being the correct answer. Without any examples of your questions, I don't know if that would be appropriate. This would also require an awful lot of extra "Clicking" for the teacher to comment on all the questions.
Another possibility would be the database activity. Would be easier for the teacher to add their comments and if you wanted it, later you could make every students responses visible to other students.