That's because she was an activist for environmental protection. Green as an adjective often refers not to the color, but rather to describe someone who is environmentally friendly. In this case, her literature fought for preserving the nature and save the environment, so it is therefore green.
The quality of the beat generation that Kerouac expresses in this excerpt is a spirit of adventure.
You can see in this passage that he is talking about his 'life on the road' - meaning that he is always traveling and experiencing new things, which was a common thing for the beat generation of the 1960s. They wanted a change, both in their personal lives, and in the world.
