The flybar is a control power amplifier. The servo acts to rotate the relatively small flybar paddles and the plane that th paddles fly in tilts... this makes the links from the flybar to the main rotor tilt... forcing the main rotor to follow the flybar.

You can have an RC heli without the flybar... there are even some mechanic sets that don't have it. Generally you'll find them used in scale models, not 3D.

There is no real mechanical advantage of the flybar being above or below the main rotor... its really just how the designer thought his linkages would work the best. There may be an argument that bove the main rotor has an advantage due to the flybar belw the rotor having turbulence from the main rotor... but as soon as you are doing 3D and flying inverted... the one with the minor advantage reverses. (and its really so minor it isn't important)