If you have seen the Disney movie Hercules then you'll understand this reference. I think Denna is to Halifax as Meg is to Hades.

There is a whole big world out there and some how she places herself to be found by Kvothe at the right times. I think (as do most people at this point) Master Ash is Halifax and he uses Denna to work Kvothe. Plus when she is probing Wilem, Simmon and Kvothe for insight on magic, I think she is trying to describe her contract to Halifax without actually describing it. I think she traded her soul for possibly her talent with music. I think she has learned things from Halifax, like how to tie Yillish story knots or catch the attention of men.