Sorry..
yeah. snapring: very important: it keeps the spring in place..
So find a matching snapring and install it.
Just take your clutch to the hardwarestore and testfit a handfull of sizes
Now for your carb:
yes, it's supposed to be only turnable by that much to prevent IDK users messing with it too much because of EPA regulations or something
And yes, that IS the idle screw.. (or pilot screw or pilot air mix needle... anyways idle screw

)
or should I say has been
IDK why Doug told you to snap it off, that was in fact a BS move,
since parts for low profile mikunis are not exactly easy to find

And even more.. there was no need to turn any further than the preset ...
(here's a breakdown of your carb in greater detail:
http://outdoorpowerinfo.com/repairs/subaru_robin_mikuni_27x-623xx-xx_carb.asp
)
When I interpret that image (on that site above) correctly, yours should have snapped just above a square part but for sure above the collar.
IF SO.. You are perfectly fine... nothing happened (you just removed the limiting cap)
get a needle nose plier and unscrew the needle .. all the way out!
Now slot the top piece to have it fit a screwdriver (clean the needle, and a bit of compressed air to also clean the thread it came from)
and screw it back in using the screwdriver...
all the way in "but gently", no need to apply force
what you want is a lightly seated needle.
and when you bottomed out, one and a quarter turn back out.
that's the stock setting.
Now sart the engine and use that screw to dial the idle speed in;
have it as low idling as possible without hiccups.
If it snapped further down the thread you're screwed I'm afraid
unfortunately not even the robin parts manual lists the pilot screw,
and thus I can't tell you it's oem part number
If you can remove it's remains though, you can measure the thread and needle distance
(best needle specs.. [length diameter].. as well)
and then trace down a part from a different carb that fits.
Good luck.
'sid