Should the pitching moment be up or down?
All points you mention are correct (for the nitpickers: Point 5 is only true below transsonic speeds). That the pitching moment of the wing is drawn nose-up is probably because it is positive this way - nothing more. The sketch you posted in your question is rather poor, with the center of gravity located behind mid-chord when it should be closer to the aerodynamic center.

Indeed, if you have positive camber, the center of pressure of the wing is behind the aerodynamic center, so the wing's pitching moment around the aerodynamic center should be nose-down. However, if you assume the center of gravity of the isolated wing to be at mid-chord, the center of pressure is normally between the quarter chord and mid points, so the wing all by itself will pitch up because it pitches around the center of gravity. The moment depends on the reference point.

Did you look at this answer for an explanation of static stability yet? Let me know if something is left unclear.