Tabbed scripts is removed in current GMS2, so don't get too used to them, I guess :P (But they will be a thing again once the 2.3 update is released, when you can define "functions" and scripts are changed into source code files)
Yes, that's correct, the different bullet types (pistol, machinegun etc) needs to have the sprite, because those are the objects that actually spawn. The parent just is a container for code / behavior they have in common.
As for making bullets always spawn in the center of the view: go into ss_pistol and ss_machinegun and change the line
n.z = z + cz + zheight*0.6
into
n.z = z + cz + zheight*0.8
and they will now be in sync with the camera.