I'm not flaming, I just don't understand why anyone would actually want a battery powered bike if an internal combustion powered bike is available. Nor only do I find them incredibly boring (to me moped, motorcycle, or even scooter, especially ones with manual transmissions, mean FUN) but their range is not even close to being what I want or need. But I understand everyone is different. I am very much into the greasy oily vintage 2 stroke type mopeds. It was my love for the internal combustion engine that got me into bikes, and then cars, in the first place.
As for what's legal, what can be used where, what kind of license if any is required, whether registration and/or insurance is required, that is usually determined by the wattage of the motor. The less powerful the motor, the less complicated things usually are. There are many differences between battery powered bicycles, mopeds, and motorcycles.
As far as I know, none of the Rad Power bikes require any license, registration, or insurance. In my state they can be ridden in bike lanes, BUT there is a speed limit of 20 mph, and that is at least twice as fast as most pedal bicycles are ridden. For some reason, I have noticed that speed is the main thing battery powered bicycles are concerned about. Their first question is invariably "how fast does it go" while my first question would be "how far does it go without pedaling"
Many places also make a difference between a "pedal assist" bike, which won't do anything unless you pedal, the battery powered motor just makes it easier to pedal, and "throttle" bikes, which can be ridden by throttle only, with no pedaling. My feeling is, if you are going to pedal, why do you need/want a motor?