How far can the sharingan go?
Sharingan by no means makes the bearer any smarter. Sharingan enables its bearer to:


See chakra of someone, but not the chakra points
See motions in greater detail making it feels like slow-motioned
Perform genjutsu better
Do sharingan specific jutsu, like Amaterasu, Izanagi, Izanami, etc.


The logic behind it is that normally humans don't use the maximal capacity of their brain, only about 10% if I'm not mistaken. In using the 2nd ability, Sharingan utilize more of the brain to do image processing, but not anything else. As for ability 1, 3 and 4, it's just that Sharingan is like a prerequisite to do so, just like a mere 160 cm basketball player would not be able to do slam dunk unless he have an ultra strong foot muscles. Sharingan is like that, only instead of foot, it's the eyes. Therefore, though Sharingan enables such feats I mentioned above, it doesn't make the user any smarter.

As for Naruto, as far as I know, Naruto is just moving very fast. His fast movement is different than that of Minato. Minato uses Space and Time Jutsu. That means Minato is not moving, he is teleporting. That's why he needs his kunai as marker.

Sharingan would not be able to keep up with it when he's on the teleportation, but when he shows up, it can.