Have you downloaded the manual (free online)?
Carb removal and clean on a GV250 - body work will be different but the rest is the same. Nice looking scoot. As the others have said there is plenty to investigate. Your English is fine and easy to understand.
In my opinion what matters and what doesn't:
Matters a lot:
Carb - proper cleaning especially the pilot jet.
Spark - ignition (electronic and not too much to go wrong except loose or damaged wires.
Vacuum slide in the carb - if it is working improperly it can kill high speed power.
Jets - must be clean and the pilot jet passage is too small and clogs easily *** the pilot jet provides a ramp to the main jet AND contributes ~15%? at ALL speeds once the main jet opens.
Tampering - because the carb clogs easily with lack of use - one year or more it may have been removed for cleaning before - look a the screws for signs that they have been unscrewed for cleaning. Very likely improper repairs have contributed to your current problems.
Wrong main jet - I experiment with larger main jets. Going too big will actually dramatically reduce power by delivering too much gas - probably not your problem but you should record the numbers stamped on the pilot & main jets.
Matters little
Valve adjustment - never adjusted valves on any motorcycle or scooter and noticed any difference before vs after.
Air filter - it is very large on the Kymco and it would really take alot of miles or dirty conditions before it would impact performance. I do wonder why with only 6,000 miles or km? it appeared very dirty.
Pilot jet idle adjustment - will effect idle and little else. have adjusted it ever which way and so no change except idle - high, low, stall at lights but no effect on the open road or highway.
Spark plug - I have yet to change a spark plug on any 4 cycle engine and see any difference. I'm wondering why your plug was dark / black which indicates a rich (too much fuel) situation.
Idle Screw - before adjusting it. Turn it in 1/2 turn at a time until it lightly seats as it will be damaged by over tightening. Record where it was set at (per the manual)
Kymco Carburetor Remove & Reinstall
http://youtu.be/uE3d9QI2m2YCarburetor Cleaning Part I
http://youtu.be/w4vW4zh8g0QCarburetor Cleaning Part II
http://youtu.be/ig0qHhdxJFECarburetor Cleaning Part III
http://youtu.be/EjCmiZ5xoeU