13d: the partial def is 'teaching' and the key cryptic elements are 'pollsters', 'working' and 'lock';
31; this held me up for ages, but there are several variations of a word beginning with N that should eventually lead you to the answer.
Thanks to those who sorted out the 'marriage' problem. I wouldn't have thought of using the method recommended. But if the clue is so unambiguous, why does it need to end with a question mark?