Nope. It can be for any number of reasons; but it isn’t limited to “because you broke a law.”
Nope. Not all police and civilian encounters involving a “stop” by the officer is an arrest. So the initial stop isn’t necessarily an arrest.
Correction. Maybe you can’t ordinarily be pulled over (validly) unless they say you’ve broken a law. But they sometimes do it anyway. Sometimes improperly.
But, sometimes, properly. For example, highway checkpoints for drunken drivers. If the cops do it to every motorist or to every random numbered (say fifth) passing vehicle, it’s legally allowed.
You’re still wrong about that. It may not be a good thing that you’re wrong. But, I am sorry to say, you are mistaken.