Okay, here's my take on "Who's in the coffin?" and "Why is Kate so repulsed by the thought of attending said person's funeral?" ...and most of this is based on an off-the-cuff comment my wife made the other day while we watched the Season 3 DVDs (and please tolerate the first observation that may seem racist, it is simply an observation based on the limited clues available in the funeral-home scene). The funeral home appears to be in a black neighborhood, as indicated by several black men seen standing on the corner when Jack pulls up in front of the funeral home. You don't see black men casually hanging out in Asian, Hispanic, or Caucasian neighborhoods (especially in a TV production, plus I believe the writers, directors, creators jammed that scene with all sorts of clues that will only become apparent as the series winds down). So that puts suspicion strongly on Walt or Michael. The coffin appears too small to be a full grown adult, so that means it has to be Walt.
Now why would Kate be disgusted by the idea of going to Walt's funeral. Well, I really suspect that Walt has been influencing the events on the island since the very beginning, if he didn't in fact create the whole "island" himself (with powers similar to Franklin Richards from the Fantastic Four). He reads a comic book about polar bears and *bam* there's a polar bear on the island. Locke appears to have a connection with the island, and the first person he befriends is Walt. Walt appears to have issues with his father, and it appears that everyone of our Losties on the island are working out father issues (as shown in the flashbacks ... only Charlie appears to be the exception to this). Michael and Walt leave the island, but Walt re-appears to Locke and tells him he still has work to do. Finally, ... Season 4 spoiler coming up:
Michael is coming back to the island, so maybe Walt sends him back (pure speculation on my part at this point)
Ultimately, the Losties figure out all their troubles are because of Walt, that Walt sent them to the island, and many of them hate Walt because of it. But not Jack; he wants to go back, and when he sees that the only one who could send him back is dead, Jack becomes suicidal. Plus, it may also be the reason why the Others are interested in children ... maybe there is some legend about how a "child shall lead them" -- hence the interest in the young Ben Linus who showed a connection to the island, and now that he's no longer a child, the others are looking for the next child that will have that connection, and they just start grabbing all the kids they can, or start trying to reproduce their own (but can't).
(Granted, I still don't know what the hell the Monster is, or who was sitting in Jacob's chair?)