I reckon the answer to my follow up question is "a. Yes" but only if H and Mary agree to put in different lists of answers so one of them is bound to be right.
Working: We know that H has one wrong, Mary has one wrong, and they are not the same. So that means that they have right answer in common. I'll call that answer "A" and the other answers give different letters. So:
Question. 1 2 3
Answer H A B C
Answer Mary A D E
We know that H has got one wrong. He guesses it is Q2 and so resubmits his answers as A-D-C. Mary must guess the other way and suppose H's answer to Q3 is wrong so she must answer A-B-E. Both possible combinations are thus covered. One must be right.
I think.