Person of interest does have a meaning, but it is not an accusation of criminal involvement. He may merely have been a witness to an act of criminality, but he might provide interest to the authorities.
It usually means suspect, but not always.
No, once you have formed the idea that the person is involved they are a suspect. They might interview him and find out he was frightened by a mountain lion and running for his life. And be able to prove it. In that case he would be downgraded from suspect to witness possibly but guaranteed, if police contact him and start interview him they will read him his rights. That is because they have already formed in their mind that he was involved. There is no difference tween a suspect in a person of interest. Give me the detail if you think otherwise
You will not be able to find a DOJ, or court established definition of Person of Interest. It’s nothing more than a politically correct term for suspect.