EDIT: This is in response to Omphalos' post above... apparently the post just preceding mine was being made at the same time I was entering that below....
Okay -- let's see if I can answer this properly. Not because I expect to change your mind on this -- or am even interested in doing so, really; but because of simple interest in the subject and a chance to, in writing about them, clarify some of this in my own mind as well as possibly putting something out there of interest to others.
Taking the last question first: On a strictly literal reading, difficult though not impossible to explain. However, any figure, whether it be a character, landscape, etc., can and often does work on many levels simultaneously. In the case of Bombadil, I see him as such a personification or embodiment in a very substantial, if symbolic, way. I am not talking allegory here, as Tolkien's distaste for that is well known. But he certainly didn't object to the symbolic importance of things in his tales; if anything he was somewhat prone to celebrate them -- fittingly so, for someone with his religious leanings. Tom, if you will, is the "spirit" of Middle-earth wearing a human face. By his long existence -- apparently since the very beginning of Middle-earth, and totally unrelated to any of the actual races inhabiting it -- he, in a very real sense, embodies that side of existence which humans (and other sapient species) tend to ignore or fail to see; Nature outside of our own concerns, as it were. Yet being a conscious and intelligent being, he is, too, aware of the part of men, dwarves, elves, etc., in the long history of Middle-earth, and this, too, is reflected in his ponderings and statements here and there. But by his rather aloof, removed aspect, he (symbolically) puts these things in perspective... much as later, in the tower of Cirith Ungol, Sam has something of an epiphany of how even the Shadow is a very small thing in the overarching tale of years.
So, to me, Tom both embodies that spirit and yet is both contemporary and ancient. And, as I said, by the little touches with Tom, both the hobbits (and the reader) get some glimpse, accompanied with a sort of
frisson of dim recognition, of those who have gone before, yet whose stories are also a part of their own.
Therefore, I would argue that Tom fulfills several different purposes, and his presence in the story brings many things out which otherwise would have been lost; things which enrich the story by adding to that experience of historical depth and emotional connection to that history; foreshadowing various connections which become explicit later in the narrative, allowing attentive readers that pleasurable recognition of the fulfillment of a pattern; he serves to render much that would otherwise be alien or difficult to get across in any emotional context something we can connect with and feel as part of the flow of the life of this place we are in; he himself is such an odd enigma that it adds to the layers of complexity of Middle-earth (not reducing it, as you seemed to indicate earlier) -- after all, Tom is very much a riddle which cannot be solved (or, if you don't mind the pun, read) because some things simply are beyond our grasp, and always will be. We can speculate, we can wonder, but we quite likely will never have the true answer. I think Tolkien intended him to have that dimension, too.
As for his being "unfallen"... Tom remains as he always has been. He is not affected by what has gone before because of his basic nature. And Middle-earth itself is not "fallen", though it has been darkened and bruised, both by Melkor and then by Sauron. It is imperfect rather than the perfect vision of the original theme of the Ainur, but it is far from being "fallen" in the usual sense. Tom, if you will, is a bit of that which has not fallen; as such, he simply has no interest in these burning issues because they have no relevance to him and what he is. In this way, he is a glimpse (but a glimpse only) of what it means to be "unfallen"; and that, too, has its resonance with many of Tolkien's concerns.
At any rate, these are a few random thoughts of my own on why Tom does belong in the tale. He is a difficult little conundrum, and certainly not going to be to everyone's taste; but I find him an oddly fascinating figure because he is such a complex, yet simple, enigma... simple in manner, but not necessarily in matter, as it were.
I hope I have been coherent here... I'm bushed after a long day, and I'm none too certain I have been. But I hope I have gotten across some of what I see there, and that it proves of interest at least for purposes of discussion or debate. And, if I have failed to address any points from the above, chalk it up to sheer exhaustion at this juncture....
