“does tinkerbell have something to do with green representation”
I have no idea what green representation is, and Google has failed me. So… maybe? Maybe this refers to environmental themes or environmentalists? If so, you could probably find that in the movies. The whole design is very nature-y, the fairies all work with nature, etc.
“does tinkerbell have any sociological concepts”
Aside from possible environmental themes? Sure. Most things do, really… Here’s an unscientific list:
- Gender. There don’t seem to be strong gender roles in Pixie Hollow, but there might be some interesting meta-level analysis. For instance, although all the talents are co-ed, the other talents are shown as pretty and more “feminine” in contrast to Tinker Bell’s talent that’s housed in the folksy and slightly-oafish Tinkers’ Nook.
- Activism. Or the lack thereof — I’ve written about that here.
- Discrimination. Even caste systems, and whether or not Pixie Hollow has one.
- Economic structures. Is anyone paid in Pixie Hollow? If not, why not?
- Legal and governmental systems. Pixie Hollow seems to have a lot of random laws, some of which are made up by the monarch.
- Possible LGBT+ characters. Some people headcanon Clank and Bobble as a gay couple since they live together and are generally linked, always seen together, etc. Personally I think that’s thin evidence, but certainly a topic of discussion.
I’m a big fan of movies as examples, so I hope that helps!