I would not worry too much about the diameter as I see conflicting data on different sites regarding this issue. Anywhere from 35.5mm, 36mm, and 37mm. Your coin looks to be authentic and in VF condition. 36mm is probably where this coin should be officially anyway and not 37mm as shown on the Numista page.
Edit: The above comment @ 36mm pretty much confirms it for me. Perhaps a change request for this coin should be made.