Since you haven't received any responses yet, here some answers from old r/AskHistorians threads that you might find interesting. On the subject of prisons, u/agentdcf and u/kyleg5 explain how imprisonment came to be used as the primary punishment for a wide range of crimes here ...
... and here.
On the subject of police, u/shreksualexperiences and u/nilhaus explain the origins of American police forces and contrast them with earlier institutions that engaged in law enforcement such as night watches, slave patrols, militias, sheriffs, and constables here ...
... and here.