I remember seeing somewhere that most modern engines use NO fuel when you are coasting in gear. I.e going down hill in 6th gear but with foot off the loud pedal. Where as if you knock the car into neutral going down hill the engine has to use fuel to avoid stalling. Please feel free to ridicule me if I'm wrong. 
No, you are correct (sort of). The engine map will see that you do not have your foot on the pedal when in gear and use a very minimal ammount of fuel, to say it uses NO fuel is just plain silly lol (engine would cut out . . . . ).
Nope. In ALL modern fuel injected engines (petrol, and electronic fuel injection, before anyone gets pedantic), when the engine revolutions are higher than the expected load requirements from the ECU and thottle position sensor, the fuel delivery is dramatically reduced (and specifically on FSI engines, this is when they go into "Stratified", or lean-burn mode - except in the US, because of their shyte petrol
). However, following on from this in the same vein, when the engine revolutions are higher than the programmed tick-over/idle speed, and the throttle pedal is fully closed, then fuel delivery at the fuel injectors is completely cut-off. Zilch, zippo, nill, zero fuel is injected.
What keeps the engine turning is down to simple physics - called kinetic energy. Imagine pushing a beach ball off the top of the cliffs at Beachy Head, once its over the edge, does the ball stop falling when you stop pushing it?
Where as if you leave it in N it will use x ammount of fuel to keep the revs at tick over.
Correct.
