How you have it in the picture is spot on.
Yes, a bit of the rotary throttle control in the carb pushes one pin into the other.
No they are not the same. One is longer and has a machined down bit in the middle for the inner grommet. the longer one pushes into the body, shorter one goes through the side. if they are not both in you won't have a kill switch.
yes spark plug on the head would work fine.
If you wanted to, take the governor cap off, and take the diaphragm off, and you will see the stop switch working.
Without disassembling it you should see it work, the inner pin will move when you put the throttle to stop
