Olivia says she illegally ran her own DNA. It is not illegal for the police to run the DNA of a person who voluntarily submits a sample. This includes samples submitted via a can of pop kindly offered to a thirsty suspect, then kindly "disposed" of by the police. Olivia voluntarily submitted her own DNA sample. It was not illegally run. The fact that familial DNA cannot be used in court is a separate legally issue.
When the team is watching the prison tape, the subtitles say that Fin is asking the questions. You can clearly hear that it is not Fin and likely another actor.