How can I fix my cursor moving more than 1 pixel at a time?

Actually.. in basic. this is what called mouse resolution. pretty much defined with DPI. for less resolution mouses it can move more than one pixel at very very slight move. with more DPI it can move even less than a pixel..

gaming mouses pretty much come with adjustable DPI and can reach 10K DPI. i'm using 3K DPI mouse and its working pretty good with my screen.1920x1080

Of course you can just adjust your sensitivity in the game options