The extra time is probably due to inputting the flight plan and clearance into the FMS.
The first flight of the day tests (auto-fx, governors, gnd idle stop, etc.) are usually performed in a remote area due to the extra noise and prop-wash they produce. A considerate pilot would not do those in front of the marshal or near the FBO.
King Air aircraft do not have APU; and, having an inertial navigation system would be the exception, never seen one installed, though I believe it was an option in a different century.