I only have my technician so I can't do 1500 watts. =P I can at my school though, they have a class license.
The autopilot is built into the flight computer on the aircraft, there is no base station computer.. well except my laptop, but that's only there to record video.
It has a GPS and you can program way points into it in a mission planner or on the fly, and it will fly to them in sequence, and can initiate special actions upon hitting them, such as loiter, circle at X radius, etc.
The last and most important and useful feature of the flight computer is return to home. If you lose signal or hit the panic switch on the radio, the plane will fly to a pre programmed altitude (you set it to be above any obstacles that you will have potentially between you and the plane) and it will fly to where you turned the plane on and circle above at the altitude until you get radio contact again or the battery dies.
Usually this is fine because say you are flying and dip behind a mountain and lose the link, it triggers the fail safe return to home, shoots above the mountain, and then you have the link again and just carry on.
The go-pro on board does hold its video, and the flight computer stores its gps position in x y z coordinates every second, and you can load that file into google earth and have a 3D line painted in it to see the path your plane took as well as speeds and telemetry at the various points.
