Gundernak, your post is a bit confusing but I'll try and answer. Oh and all this is based on my memory of Aerodynamic and you really should double check it to make sure I'm right.
"These are 4 statements on L/D max and AOA for max L/D:
1) L/Dmax AOA produces the minimum total drag
2) At L/Dmax AOA, parasite drag and induced drag are equal
3) L/Dmax AOA produces the greatest ratio of lift to drag
4) L/Dmax AOA is the most efficient angle of attack"
As far as I'm concerned statement 1 and 3 are the same thing: At L/Dmax in straight and level flight the Lift produced by the wing equals the weight of the a/c and therefore is a constant. Thus the only variable is Drag, so you get L/Dmax with the minimum total drag, therefore also the greatest ratio of lift to drag.
Statement 2 is proved by this graph (from wikipedia)
http://upload.wikimedia.org/wikipedia/en/1/12/Drag.jpg
Now for statement 4. In my mind an angle itself cannot be efficient, however the AoA at L/Dmax allows the aircraft to operate at it's most efficient in regards to time (in regards to distance you want Vminpower which is a different speed).
You say near the end: "Now you can see at level flight at speed Vmd the L/D is max. But the AOA is not the L/Dmax AOA of the aerofoil." However, when you look at your own results the second sentance you've written is wrong
AOA: 3 deg - L/D: 14,5
AOA: 7 or 8 deg - L/D: 15,5 (max L/D)
I don't know where you found out the L/Dmax AoA of the aerofoil but you've disproved it with your own test... unless I'm missing something.
Dit