My cursor doesn't show up once I move onto the canvas (but it shows up fine on the sidebars), and if I make a mark it doesn't show up on the screen unless I right-click afterward.

Hi abeth,

If you go to Settings > Configure Krita, check your cursor shape and outline shape. Perhaps you have No Cursor / no Outline selected, which hides the painting cursor entirely.

That made it so that the cursor does show up on the canvas, so that's half of my problem gone, but the canvas still doesn't "update" until I right-click. Even if I make a selection, the "marching ants" effect doesn't actually move, but the position of the moving dots "updates" once I right-click.

You might have a broken display driver, if you're on Windows. If that is the case, you can either update the display driver or disable OpenGL.