North star is 100% on the north pole. I mean magnetic pole.
No, it is no where near the magnetic north pole.
Because nasa/google north pole is not real north pole but just a prediction has not meaning.
No, it has real meaning.
It is the point where Earth's axis of rotation passes through the surface. If you want to go the FE route, then it is the point where the north celestial pole, where all the stars appear to rotate around, is directly above.
The pole star is not as high as it is supposed to be, and after a certain distance due to the "angular size" problem that has already been revealed by me, objects of certain heights disappear on the horizon.
That doesn't apply to lights, and doesn't make it disappear at the horizon.
As an object goes away and gets a smaller angular size, it will eventually be too small to resolve. If it is close enough to the background in appearance it will vanish. But if it is different enough, e.g. a bright light against the black background of the night sky, it will still be visible, and appear larger than it should. To have the stars vanish you need to have them get far enough away for them to be so dim they blend into the background.
Telescopes and the like also allow you to see further than you otherwise would.
So no, Polaris, being a star viewed at night, will not disappear due to angular resolution.
Even for objects which do disappear, they will disappear at whatever height they are at, they wont magically be brought down to the horizon. This means Polaris should still appear quite high on the equator, and even in the southern hemisphere.
The only way out is to have light bend.