Fry - Party Like It's 1999 (obviously)
I think you mean
Walkin' on Sunshine.

Professor Farnsworth - She Blinded Me With Science
That's a pretty good choice, but I prefer this one:
Science Fight, by Consortium of Genius.
Hermes: Buffalo Soldier - Bob Marley
Perfect. Nobody else pick anything for Hermes!
As for Zapp, the chorus of
Unchained by Hammerfall would probably be something he'd play as he sent wave after wave of his own men to their destruction. But for theme music, I think that the
major themes from
Mars, Bringer of War by Gustav Holst seem appropriate as leitmotifs.
Then there's
this little blast from the past that seems to sum up the Fry/Leela ship prior to the movies.
This could be a really good thread.