Looks like typical vignetting, nothing to worry about. It should go away as you go a bit past the 16mm end of its range. It's probably perfectly normal, and I only say probably because I don't own that lens.
And yeah, the shadow in the bottom center looks like it was cast by the hood, by your flash. That's pretty common, too. Wide angle hoods and pop-up flash don't do well together, even some external ones don't have the height to properly clear the hood.
If in doubt, remove the hood and reproduce the shot. It should be clear by that.