Don't press the "don't allow anonymous answers" box, post the question without being anon, then post an update on the question, but tick the box underneath which says "anonymous". This'll make your question go anonymous.
No, there isn't. You only get one chance to make that choice, and that's when you're making the question. Once submitted, that's it. Also, it's not fair if you can go anon but everyone else has to show their face. Hypocritical, if you ask me. That's the reason why you can't go anonymous while not allowing anon opinions.