My 125cc twist and go scooter's number plate started melting

Most 125cc scooters are restricted to between 60 and 70 mph often because of certain laws in each country they are sold in. These 'Twist and Go' automatics alway sound like they want to go faster but the transmission needs to rev that high to work properly.
It is possible to de-restrict your scooter but the top speed you would get would not be a lot higher, maybe 10 to 15 mph more.
Scooters also use much smaller wheels compared to a motorbike which makes the scooter less stable at higher speeds. Mine starts to shake and vibrate when it hits it's top speed of 70mph. To get much higher speeds you would need to spend a lot of money changing gearing ratios roller weights or even swapping complete transmissions. One option if you want to keep at the 125cc size is to change to a bike with a manual transmission like the bigger motorbikes. Some of these bikes can get closer to 100mph but most 125cc bikes and scooters all tend to max out at 70mph. At higher speeds the manuals don't sound like they are working as hard as a scooter does.

2003 Honda Dylan SES 125 Scooter Engine ebay - YouTube

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https://www.youtube.com/watch?v=DzAByfS2OAY
Nov 21, 2012 - Uploaded by TheShamefulsin
Short video demonstrating a 2003 honda dylans engine, that it starts and runs for the purpose of selling the ..

honda dylan in United Kingdom ' Motorbikes & Scooters for ...

https://www.gumtree.com/motorbikes-scooters/uk/honda+dylan

GumtreeMy 2003 Honda Dylan ses 125, unfortunately it was stolen from me, hence the .... uk plate GF07 XJK,bike has only few scratches, last time I could not start it, but ...

I don't have the manual on had for the scooter, But the jerking Your experiencing above 40mph sounds to Me like it's due time for a carb cleaning, I'm not sure weather Your scooter is a 2 or 4 stroke so, If its a 2 stroke, You will either mix the oil with Your gas or look for a separate oil tank, If its a 4 stroke, Then it should have a small dipstick on the side of the case where the oil should go.

BAD STATOR MAGNETO ALTERNATOR DISCONNECT NEGATIVE AND IF BIKE IS STILL RUNNING THEN ON IF NOT NEED TO REPLACE IT

have you replaced spark plug and air filter

Where is the mixture screw on the Habana custom 125cc year 2000ish please?

This scooter has an S drive controller. The beep code will begin with 10 very fast beeps followed by a number of slower beeps. The number of slower beeps indicates the actual code. It will do this only once. To repeat the beep code, remove and reinsert the key.
Beep code #9 is a possible controller trip.
Diagnosis:
The key may have been inserted during battery box installation.
The controller may be overheated.
The brake is dragging or pulling too much current.
Solution:
Remove the key from the key switch before installing the battery box.
If the problem persists shut down the scooter for 10-15 minutes and allow the controller to cool down.
Bottom line is that you may need a new controller or brake. Keep in mind these may be warranty items. A qualified technician may be needed to diagnose and repair the problem. Hope this helps.

Sounds like it is running too lean. Look for an air leak around the carburettor manifold.