I'm new too, so take my opinion with a grain of salt, but I think you're right with one minor correction:

    name::{body} :" function declaration

This isn't necessarily niladic or monadic or dyadic on it's own, it depends on the body. The bodies from the example all just happened to be monadic.

    +/x          :" monadic : sum over argument x
    #x           :" monadic : count of the argument x
    +            :" dyadic  : sum
    !10          :" niladic : an array from 0 to 9

I had to look up how calling a dyadic function looks in Klong:

    add::{+}
    add(2;3)