1. The fact that something wasn't around at the time of the founding doesn't make it unconstitutional.
2. The creation by states of police forces violates no provision in the constitution.
3. Federal "police" agencies like the FBI are established by laws passed through congress.
The only real meat here is the question of whether the vast network of agencies that are under the executive, but have many quasi-legislative (rule-making) and quasi-adjudicative (judicial) functions are unconstitutional delegations of power. Of course, that is rather moot because there simply is no way to have a huge country like America operate as one nation without executive agencies.