SwingDJs

Second song is "Rhythm Is Our Business", but I don't know the artist.
Third song is "Madame Dynamite" by Eddie Condon.

And I'm pretty sure the first part is "Boogie Woogie" - edited quite a bit - by Albert Ammons.

The second song is identified on the youTube page. It's "Walk That Thing" by Charlie Johnson and His Paradise Band.

Well, the last one is "Jumpin' at the Woodside" by ??? I'll have to ponder on the others.

.. or maybe that IS the "original"... ?

I don't know where the original is from, but here's a song that samples it:
http://www.youtube.com/watch?v=Wrqj3NDnv5Q

Not working for me either...

Kinda sounds like Buck Clayton to me. Don't know the song though, sorry.

I also like Jo Jones's version.

Yes, "Close Your Eyes" by Humphrey Lyttelton & His Band

The song is "Zonky", but I don't know the artist for this version.

It's "Baby Won't You Please Come Home", but I don't know the artist.

It's 'Dance Of The Sugar Plum Fairy" by Tchaikovsky.

According to dbopm.com ("Database of popular music"):
Song title: Wham (Re-Bop-Boom-Bam)
Country of origin: United States
Words: Eddie Durham/Joseph 'taps' Miller
Music: Eddie Durham/Joseph 'taps' Miller

... great first line: "Where have I been hiding all your life? ......."