Just how accurate is this database? If someone has violated probation or has a warrant (nj), it would be shown when ANY police officer in ANY state ran that name right? My kid thinks she has a warrant but has come in contact with the police a few times (boyfriend-domestic) and a traffic violation, so what gives?

Yes cops can definitely find warrants for you , even if they are out of state, when you get pulled over or whatever. She must not have any.