Al. tells everyone to throw away their CNS carb, I'm not quite sure why...
The CNS is a bit harder to understand and tune than the basic NT or speed carb, but they are good carbs when tuned properly. Here is some basic info.
The standard NT or Speed carbs have a single fuel jet and an air choke on the carb. The CNS carb has a main fuel jet, an idle fuel jet, and an "enrichment jet" which is attached to a lever which richens the fuel mix for cold starting (in place of an air choke. Some scooters use the enrichment method rather than an air choke, often controlled by an automatic plunger rather than the manual lever on the CNS). So the CNS IS more complicated than the NT or Speed carb.
Things I have noted about the CNS, the idle jet is VERY SMALL and can clog easily. This will cause hard start condition and rough running in lower RPM range. I use a very thin wire (wire brush bristle or bare wire from a garbage bag twist tie) to ream through the idle jet when I clean the carb because carb spray had not been effective for me. When your kit is freshly installed you might get a little debris down your fuel line that could easily clog this idle jet, so make sure you keep it clean. If the carb is sitting off level you might need to adjust the float to get her running right. The main jet might be a bit small...
I have a CNS V2 carb, slightly modified at this point, haven't had one of the V3 in my hands yet.... That said, the three tubes you were asking about, the bottom one is the overflow, keep that tube pointing downward where it can drain away excess fuel if there is overflow. The other two just need to be open (connected to nothing). On my V2 carb one of them go into the air filter, I originally had the red plastic air filter, while your V3 should have a high flow cone style filter. Also, I hear the air mix screw is capped off on V3, and may be screwed in fully under the cap (a turn or two out would normally be a better position). Someone had reported that the cap comes off easy enough by drilling a hole in the cap and prying it off, then you can get at the air mix screw.
I don't want to go into giving tuning advice before you post feedback on how she runs right out of the box, so post back on how it went and we will try to help you get her tuned up...