2002 Mazda protege. Shifter cable broke from the selector lever (i believe those are the correct terms). Anyone have an idea of how I might fix this?
From the photo angle it looks like you need a new shifter cable and a new “manual lever” for the transmission.
Those usually come as a unit so you will be replacing from the clutch pedal back most likely .Probably a Mazda only part unless you get real lucky and find a used manual Mazda in a junkyard .
It’s not a stick shift car
You can clearly see the automatic transmission pan in the picture 
Well yeah, plus you can see that the lever only slides in one direction, which would be further evidence that this is an Automatic.