After the arrest of an individual at a school which has already seen a fatal attack is made based on an allegation of threats and a firearm being brought by the arrestee to school, why should this information be kept from the students, teachers and parents at that school?  

What is the liability of the school if it is?  

Are the police allowed to incarcerate people in the US without that knowledge being public?   

The US Constitution has something to say about that: "The writ of habeas corpus,  is an order to require a person holding a prisoner to demonstrate the legal and jurisdictional basis for continuing to hold the prisoner. If there is no legal basis for detention or incarceration, the court orders the release of the prisoner."

That can't happen if no one knows he is in jail.