This product does not have a decibel rating. As it works by convection, meaning there is no fan, it should make little to no noise. As to your second question that would depend on the length of the run, the wire gauge and most importantly the electrical code in your state. Thus you would need to speak to a local qualified licensed electrician or the electrical inspector in your municipality.
Yes, I bought mine from homedepot with the optional thermostat. Basically, it's the one that does not say "also available with optional thermostat". HD really needs to do better job on the online descriptions of most everything.....