1) It's an acronym for the dread "Committee on Public Safety" that wreaked havoc during the French Revolution.
2) The initial shields worn by uniformed policemen in nineteenth-century New York were made of copper.
3) They got the name from David Copperfield -- the Dickens character, not the magician -- who aspired to a career in law enforcement, idealizing the day job of a decent and humane beat policeman, but who was tragically prevented from reaching his goal by the machinations of Mister Macawber and Uriah Heep.
4) In 1876, a London bobby, also known as a peeler-- both names deriving from Robert Peele -- was sipping a concoction consisting of eight parts gin and two parts vermouth. This put him in such a good mood that, when the waitperson returned with a refill, the randy fellow smacked her bottom, "copped a feel," and went home sheepishly with a black eye. His wife asked him what happened. He lamely said he had walked into a door. "Rubbish," she said. "I bet you went to the local and copped a feel." The fame of the anecdote was legendary and the man on the beat never did get credit for the modern martini, which he had accidentally invented. ND "copped" shortened to "cop" lives on.
5) The coinage is John Milton's from Paradise Lost, Book XI, as Adam gratefully accepts the knowledge that his future offspring will redeem the race. "Peace returned / Home to my breast, and to my memory, / His promise, that the cops shall bruise our Foe; / Which then not minded in dismay, yet now / Assures me that the bitterness of death / Is past, and we shall live."