Is it possible that a load can be destroyed if I am disconnecting all other loads in the circuit but one?
In my understanding the current which would normally spread to all these consumers would then only flow through the remaining consumer ...


No. The battery voltage on your scooter will remain almost constant. Each circuit (consumer) will draw only the current it needs.


  If you disconnect the rear blinkers, then the front blinkers are way faster, so I think it is because more current is flowing through it.


No, the blinker relay is designed that way so that you get a visual indication that one of the bulbs has failed. It is blinking faster because less current is flowing.


  So if I disconnect the ECU (36) in the following circuit then I guess the current is very high on the remaining components.


No. The battery voltage will remain the same.


  I thought the fuses would blow in this case, but I had the case were the plastic of the fuses was just melting but the fuses stayed alive after I had a shortcut, almost all consumers were disconnected at that time.


"Short circuit" is the correct term but it is not clear what situation you are describing here. If you have a short circuit before the fuses will not blow and maybe the fusebox will get hot.



Battery voltage will normally drop a little when you increase the load. On a car, for example, with the engine idling you might see the lights dim a little when the wipers and heater fan are turned on.