It's not an E2, because you can't be achieve the anti-coplanar transition state.
E1 seems likely because the electron-withdrawing oxygen will stabilize the carbocation, and it's also 3°.
You are correct about the second part though. You can protonate your C=O bond, and put a positive charge on the carbon, but then I'm not sure where you would go from there. No matter how I draw it, you are short a hydrogen from somewhere.
Are you sure there aren't any other reagents in the mechanism, that it is run in neat pyridine? Or even more, maybe it's pyridine hydrochloride, so it's actually an acid-catalyzed mechanism?
Azamanam, really interesting thought, I like that synthesis technique as well. I also cannot get past the iodonium ion. There has to be a missing piece of information.