Well, it's not the do all, end all, but we can start with this
Wikipedia entry.
You notice that laws vary wildly. Florida allows a 60 mph top speed, Other states have no rules.
As to your thoughts on registration: In most states bicycles, even motorized bicycles, are NOT considered motor vehicles and therefore are not covered under uniform registration laws pertaining to motor vehicles.
Many states seem to be making up the rules as they go.
You'll notice in the Wikipedia article that most states that actually have statutes restrict bicycles to 3 wheels.
As a dealer for EZ Motorbikes-- a 50cc ICE motorized bicycle-- I am in contact with dealers from all over the USA and Canada and have heard some horror stories.
And in case you're wondering, the 2001 Federal Definition of a bicycle was said to be an obscure passage in VP Dick Cheney's Energy Bill. In other words, it was written by Big Oil.