I'm making a Hexblade warlock with Polearm Master, and I'm thinking about getting a level of fighter for the Dueling Fighting Style.

I have some questions about how these interact with the Eldritch Smite warlock invocation:

 - Does the Dueling fighting style boost Eldritch Smite damage?
 - Does Eldritch Smite get bonus damage from the 1st-level Hex spell?
 - Does Eldritch Smite get bonus damage from the Hexblade's Curse
   feature?