Access and authorization are separate concepts. You can't trespass on someone's property just because there is no gate.
This is why companies put authorized use only login banners on servers and network gear.
No. If it is public, everyone is authorized.
Sorry, not the case at all. If you start poking around on a server that the DoD forgets to lock down, you're going to jail. You're not authorized to use it just because you can access it.