Your examples of angles of attack do not quite fit in with a lot of models. Take for example my 3D profile planes which have no angle of attack, the wing section and tailplane being exactly parrallel.
Actually, AOA is the angle of the wing to the airflow. What you're describing there is called incidence. The angle of the wing in the fuselage is the angle of incidence. Same name for the angle the stabilizer is built or trimmed into the fuselage.
How then does it create lift that is not cancelled out by the inverse side of the aerofoil?
The airfoil isn't parallel to the airflow when a symmetrical airfoil is generating lift (right side up or upside down). A symmetrical airfoil be it a flat plate or any profile, starts generating lift as soon as it's pitched away from it's zero lift line. If it's flying perfectly level, it won't be creating lift either above or below the airfoil. Pitch it either noseup or nosedown and it'll instantly start generating lift.