The riding skill has only an influence on horses speed and maneuver. For each skill point in riding you have above the horses requirement its 5 %. You can check this yourself in native Singleplayer, ride around alone, spend more points in riding and your movement speed even on the campaign map gets better. Do the maths.
(Why would it increase horses armor or health points? Doesnt make sense).
On your build, it depends (as always) on your playstyle. Do you fight against other cav, or mainly against footmen?
For a sneaky horseman that loves to stab infantry the goal should be the one stab kill.
For a duel-cav you want as much maneuver and speed as possible.
(so no bonus if I ride plated charger with skill 6, but if I ride with skill 7+ then I get bonus, simultaneously, no bonus for riding courser with skill 4, but bonus if I ride with skill 5+)
Exactly. This. is how it works.
The bonus is applied like the shield one I believe, so, simply by having the requirement for a horse at 5 you are already getting a bonus, which is why some cataphract/chargers can even outrun and outmaneuver palfreys/rounceys/destriers. Aside from speed there's also the HP and armor bonus, which are always appreciated for keeping your pony alive for as long as possible.
You believe wrong. It would be easier to get along if people like you stopped spreading rumours/ totally wrong "facts" to confuse other people, for fun, intended, or just careless.
With shield, you might be right, since there is no shield requirement in native, but with riding you are wrong.