“By what authority does the federal government insert itself in to an issue that is clearly a local/state matter?”
The usual cover story is that it is conducting a federal civil rights investigation.
There are two sets of laws at play here; state law and federal law.
Yes.
But the way it is supposed to work is, the feds only get involved in a local/state case if it appears the locality/state permitted or perpetrated civil rights violations during its handling of the case.
In this instance, the state has not even concluded its preliminary investigation, never mind reaching any conclusions.