Sketch automatically organises Symbols into folders when you put a / in the name.
Haha. You beat me to it.
Pretty sure Sketch will export your assets into folders if you have a / in the name as well.
"button/green-solid' isn't that great of a name. Button/primary, button/secondary works better since you can change the color of the button at any point in the design. It will get confusing when you have a button called "green" that's actually red.
Agreed. IMO the use of child symbols are great for 'states', e.g. '/normal', '/hover', '/active'. Naming them as specific as the color of the button limits yourself in the future of altering that buttons color