Your Zones are a bit messed up. The English counties all appear to be in there twice for example. And initially you get no counies offered, because you're defaulting to United Kingdom which has no zones attached. But those are peripheral issues.

I suspect that the reason that you are getting both dropdown menu and entry field is because Template Monster have messed up the javascript that ensures that only one is displayed at a time. I checked their demo of this template, but they had the dropdown facility turned off, maybe for this exact reason!