In a similar vein, the b13 (as seen in bar 6) is another chromatic extension (so C7b13 would have Ab as the b13) which helps generate a lot of interest.

You can think of bars 2-3 as essentially V-I with C7b9 resolving to Fm7.

This C# is what we would the b9 extension (think of D as the 'natural' 9th to C), and it's a very powerful chromatic extension to use on dominant chords to create lots of tension before resolving. have you worked it out? Edim7 is functionally very similar to a C7 chord (C-E-G-Bb) with an additional note, C#. If we think about that Edim7 chord, it looks very familar to a dominant chord with the root of the chord taken out. Why on earth are these horrible chords in a Christmas song?! Remember how important V-I cadences and extended chords (such as a 'dominant 7') are in Jazz? These extensions help create additional tension and colour to the chord progression, which makes a simple V-I sound far more exciting to the listener.