I really like my Kinetic. Really bright lights, really nice brakes, performance and stock parts (Vespa) for days, one of the best ignitions on any moped ever, decent suspension. My advice would be to go ahead and loctite everything and get some better rear shocks.
Go ahead and clean the outside of the head right around the decompression valve.
The goal being to see if oil/shit leaks from around the decomp and thus the lowish compression. The other thing is that cheap compression gauges suck. I am not one of those, "buy only the most expensive tools" guys but Harbor Freight compression gauges suck. They just make shit up.
As for the no idle I would bet its the carburetor.
There is a little hole below the main venturi there. I am pretty sure its on the shim/intake side but I am not 100% sure without having one in my hand.
It is straight up tiny. Like you have to blast it with carb cleaner and blow it out with air and if you want to poke it you need to use a strand from a spun brake cable.
If its a 13mm SHA that means someone was trying to do performance upgrades so its possible other stuff was fucked with.
I also had a coil go bad on a Kinetic once and it had a kind of weak idle before hand so thats something to try if you have a spare coil laying around.