Are the police allowed to act on charges and arrest individuals? Or is this just a complaint?
Yes. Although the arrest can happen before the charge, typically a judge will issue an arrest warrant as soon as the charges are filed.
And given the >90% conviction success rate in the USA (at least in federal cases), it's a pretty good bet any charges filed will stick if the prosecutor wants them to.
Prison is where people who are convicted of felonies (crimes worthy of >1 year in custodial sentence) are sent. Jails are where people awaiting trial, or convicted of misdemeanors (crimes worthy of <1 year in custodial sentence) are sent.
Prisons are run by a state or by the Federal government, and are for holding persons who have been convicted of a crime and sentanced to a longer term.