In terms of the characterization, I think I can provide a broad enough picture. You might have to go back and find evidence from the work to prove the depiction/ characterization offered. Although born of white parents, Cooper depicts Bumppo as one who is in sync with nature and the natural world. An American Transcendentalist, Cooper was very passionate about the idea that humans must have a reverence and healthy respect for the natural world. Bumppo represents this, as he lives off of the land, showing complete respect for it. Cooper wanted to create Bumppo as one that merged the best qualities of the Native Americans in a white Frontiersman, foreshadowing Cooper's hopes Westward Expansion which was to come. Bumppo is a very complex person in Cooper's depiction. He life is one of choice, as he was not tossed out of traditional society, but rather chose to live the life he leads. In being of White society, Bumppo seems to be a link between the growing world of accepted "civilization" and the Native American world. It seems like Bumppo has found the answers as to how both can coexist without one controlling or dominating the other. Bumppo lives in accordance to rules and understandings ("One shot, one kill", take only what you need) and has found a niche where one can live within oneself and respect the natural setting.
I think this characterization is bolstered when you are able to go back to excerpts from Cooper's work to find where we can see these ideas developed more.