In the excellent (if rather terrifying) The Doomsday Machine: Confessions of a Nuclear War Planner Daniel Ellsberg describes going to see Dr Strangelove and basically concluding that a lot of the movie was pretty realistic - particularly the delegated use of nuclear weapons by a base commander without the approval of the President. This was actually possible for a long time even though publicly it was always said that only the President could authorise the use of nuclear weapons.
Yes. I think as early as Truman or Eisenhower the president would authorise the use with discretion delegated to local commanders, though I think there were some general rules of engagement attached to authorisations.