Failure to id is a secondary crime, you first need to be lawfully detained/lawfully suspected of a crime, before id can be demanded in 24 states. In the remaining states you need to be arrested before id can be demanded. Driving a motor vehicle is different though. As long as an officer had a reasonable reason for pulling you over, they can id you even if you dispell their suspicions prior to providing ID. If you're pulled over, it's best to always provide ID.

So it's only a lawful order if the police follow the law, if they just walk down the street randomly asking people for id, then failure to comply with their unlawful demands can be thrown out by the courts. Of course the police can just lie and make up a reason they suspected you of a crime, which is why some states have made things like "smelling marijuana" not enough on it's own.

Sure, but if they demand your name, you tell them your name, they can't then demand your ID to prove it