If the questioner selects my answer as the correct one, can I still go and edit the answer or is it frozen?
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Yes, you can edit it, and so can anyone with editing rights. Just because it was selected doesn't mean it can't be improved.
When something is selected as the accepted answer, all it really does is provide a visual identifier which one the original question asker believes is the best answer or the answer that solves their problem, along with a 15 point bonus. There are absolutely no locking features on the checkmark (except you can't delete your answer...thanks Jon)