You make good points...it's just that with Father Christmas appearing as Santa it makes it rather hard to take that part of the movie seriously, when, as you point out, it is instead supposed to be a moment of great import and not trivial at all (the silliness of the situation was further emphasized with Mr. Beaver saying "i hope you've all been good" and then later Lucy quipping "see, i told you [that he was real]").
By the way, could the gifts be seen as somewhat analogous to the gifts of the Wise Men? I can't remember if Edmund was with them then or not. I'm pretty sure though that he wasn't and therefore only three gifts were given out, just as when Jesus was born.
You make a good point. The "I told you he was real" wasn't in the book. The comment was out of character for Lucy. I would have expected that out of Susan, not Lucy. Susan is a lot cheekier than Lucy. There were 2 gifts give to each the 3 children who were there. Edmond was a captive of the White Witch at the time. It doesn't match-up with the story of the Wise Men very well. It is more of an Easter Story than a Christmas Story. The story is about sacrifice and redemption.