I'll try to address each of your questions separately.
In order to display something on both the projection screen and on a monitor for the pilot, you'll want to design your air application to include both screens and to run in windowed mode at the resolution of the two screens put together. Let's say your monitor runs at a resolution of 1920x1080 and your projector will push 1024x768. This is what you would want your application to look like:
You'll want to set your Air Settings to use custom chrome, this will hide the standard window chrome. You'll also want to set the initial window settings in the advanced tab:
All of this will set you up to be able to run the application on one computer and have, in essence, two separate displays.
Now, for the "duplicating" part. What you'll want to do is have a Bitmap
in the pilot's view to which you'll be constantly drawing the parts that you want him to see, but not the parts you don't want him to see. This process is more commonly known as blitting.
I don't know how your application is set up exactly, but I would hope that your HUD is somewhat self-contained. So let's say that you have a MovieClip
with everything in it except for the HUD, here's what you would do:
var _pilotViewCanvasData:BitmapData = new BitmapData(1920, 1080); // ideally, you would make this just big enough to display what you need to display, not the actual size of the pilot view
var pilotViewCanvas:Bitmap = new Bitmap(_pilotViewCanvas);
//add your canvas to the pilot's view area of your application
addChild(pilotViewCanvas);
//add an enter frame listener so you can repaint the canvas every frame
addEventListener(Event.ENTER_FRAME, onTick);
function onTick(e:Event):void
{
_pilotViewCanvasData.draw(yourGameClip); // this is where you paint the canvas with your display
}