Could be Jadeite, Aventurine, a harder soapstone, a somewhat cruddy amazonite or something in the serpentine family (e.g., antigorite/bowenite). read more
A green mineral can be any number of things, minerals that are naturally green are olivine, fluorite and epidote. Quartz, feldspar are green some times. I left out many like malachite, that it isn't or rare. It could also be a rock of some kind. read more
The most widespread green mineral, chlorite is rarely present by itself. In microscopic form, chlorite gives a dull olive-green color to a wide range of metamorphic rocks from slate and phyllite to schist. read more