thought it was 25 mph in ohio... but either way dont get clocked going over 30 or you may be asking for it. if you get stopped: yes it is under 50cc, yes it is under 1.5 horsepower. your bike looks fine, has pedals, headlight, taillight... should be good to go visually.
the bmv never asked me for a purchase price. there is also a good chance you will get someone on the other side of the counter that doesnt even know what a moped is so make sure you know the exact model you are registering under. ohio does not keep a list of vins either. anything you give them is good enough as far as they are concerned.