1. May be it is misquotation based on 'at the drop of hat', that means: immediately at the response to a signal. May be the context would be useful.
2. A combat between two person with weapons, with the presence of witnesses.
3. 'Dictated but not read' is usually used at the end of the text worn that material has not be personally written or verified by the author.
I'm not a teacher.
Student or Learner