R.I.P. Kymco.
It was the regulator. I still don't understand the behavior - when being checked calm nothing was suspicious, it kept an innocent mask. Disconnected from baterry the resistence of it as well as of wires coming in was infinite. That's probably bcs of semiconductors inside why it could open a short-circuit when the key was on and 1) I was either pressing the start button or 2) trying to start by connecting directly the flow to the starter motor (the fuse blown in both cases) .
When I put a wire instead of the fuse and try to start: The red wire between the battery and the regulator was "boiled", among other victims seem to be the start button (checked by multimeter after the "boiling" test) and maybe also the isolation of some wires neighbouring the red one.
FED UP, I sold Kymco for a few "bucks" (euros here in France), there's no doubt it was accursed with a daemon inside, I hope I'll forget is ASAP.
Epitaph: Here in France it was not easy to find the right parts for this model. Not sure whether it's Kymco in general or only this model, but IMO it's better to pay more and buy a moto for which it's not such a loooong-time-consuming-process to find and order a piece, not to be full of doubts whether it will really fit that, and also to have a moto with a good documentation.