Yep, the long groove locates on the pin and the shorter, angled groove is where the idle-speed screw pushes on the slide to raise/lower it.
Ensure that the slide moves up and down freely.
The correct order for the parts is cable into top cap, spring immediately below, then on the slide:- First drop in the needle, then the 'C' washer, (point the open end of the 'C' washer toward the long slot), then slide the cable into place while holding the spring compressed, then release the spring. The spring will drop into the top of the slide and press on the 'C' washer, holding it and the needle in place.
(This is best done with the cable adjusters slacked right off.)
Then slide it into place in the carb body, carefully aligning the pin.
Regarding the pic, it wouldn't hurt to change the really big one.
(I only mentioned it because it's a hot topic at the moment.)