Does CPU/GPU speed affect my ship's turrets' ability to track and hit targets? Do graphics settings?
Generally not in my experience.
However, Elite tends to compensate for lag, and a lower FPS can worsen the lag. I'd say I have hit targets I shouldn't have but the lag compensation somehow made it happen. But maybe I have also missed hits missing because of lag. Others may be more observant than me.
More important, this is from a dev post 2015-06-25 Mark Allen, and I think it is not fixed: Don't turn (much), as this confuses your turrets. "it does
not account for your ships rotation when checking the target's relative acceleration."