with the key ON, your main fuse is powering all circuits, including your headlights and tail light and gauges. Thats an awful lot of drain on these anemic charging systems. These bikes don't make surplus voltage until the motor is running about ~2,500 RPMs.
As for the melted GRN wire, sounds as though someone reversed polarity on the battery or with an auxiliary jump.
If your tests indicate NO FAULT, then your components are good. Its likely your behavior that is the culprit, not the components.