Everyone who is going be a driver in a rental car has to show a valid license at some point, don't know where that is at the airport though... It's usually where you pick up the keys at other places though.
Depends on the rental company. If you are looking to show your license when you pick up the keys at National or Alamo, you are going to be showing the keys to the car. LOL. The keys are in the car doors (except for a few "hot cars").