Southwest Airlines was allowed to fly all of their grounded jets to a facility in Arizona a few weeks after the initial grounding. The FAA allows this as long as there are no passengers on board.
Sort of. All flights in U.S. territory, and by U.S. airlines anywhere in the world, are banned. Non-passenger flights can be authorized but they require either a Special Flight Permit (a specific process for authorizing ferry flights of any non-airworthy aircraft) or an Experimental Airworthiness Certificate (which you may know of from homebuilts, but in this case it's for testing design changes).[1]