1. What difference would it make in determining the origins of Christianity if the Gospel of Thomas truly pre-dates the Gospel of Mark and the letters of Paul?
If the Gospel of Thomas, with its obvious gnostic flavor, predates the Gospel of Mark and the Pauline epistles, it could further suggest a strong gnostic current very early in the Christian community – evidence that gnostic Christianity, rather than "orthodox" Christianity, may have been closer to the original teachings of Jesus. It could even mean that this Gospel was one of the sources of Mark (the famous Q document?), or that it drew on a common source with Mark.
2. If the infancy narratives of Matthew and Luke are not historical, how does this affect your feelings about celebrating Christmas?
For quite some time I've not considered these accounts to be historical narratives – yet I continue to celebrate Christmas and continue to find deep meaning in it, albeit the meaning I derive from it is of a different sort than the meaning an orthodox Christian would derive from it.
For me the Christmas story is a mythological narrative having less to do with the physical birth of a particular individual (Jesus/Yeshua) and more to do with a grand cosmic drama: the coming of Light into the world. This same narrative was common throughout the ancient world (with many deities and mythological figures being born on the exact same day – Dec. 25th) – a fact which, rather than undermining the Christmas story, actually reinforces it as a universal cosmic truth. The universality of this myth of the birth of Light into the world (reflected in nature, and key to mystical/esoteric teaching, i.e. the birth of the Light in us), releases the Christmas story from dependence on historical detail and on the existence or non-existence of a particular individual called Jesus of Nazareth, thus giving the story a potentially universal appeal beyond Christianity as traditionally defined.
3. Who do you believe Yeshua ben Joseph was at the beginning of his public ministry?
Assuming Yeshua ben Joseph was a real historical figure (and not a composite of several people, as some scholars have suggested, or an entirely invented figure), I think it is highly likely that he was engaged with mystic, esoteric, even gnostic groups – very likely the Essenes.