@Jairus : I have reasons for not wanting Jessie alive, the primary one being that it
cheapens her death and it would
cheapen any death - namely Aerith's afterwards because if Jessie comes back, why not Aerith? I noticed that Biggs' death wasn't as much a big deal as Jessie's, Cloud even implies that help can come at time to save him while Jessie had Tifa crying for her, Cloud aknowledging her, etc. Imagine seeing her suddenly "oops sorry I wasn't dead in the end", it's way too bizarre and it cheapens her own death like hell, and no one dying afterwards would have the same impact on the player because once a certain NPC who was dead was not in the end.
As for how why would someone leave a memento of Jessie in Biggs' room, well, he's at the orphanage, so I'm quite sure they know him well, probably knew her too. They grew up together, so even if people don't know them, they know that those three were friends. And since Biggs was brought to the orphanage, it's quite certain that he was brought back by someone who knew him.
It's also to note that the Gold Saucer is the place where you meet up with Cait Sith for the first time (properly, at least), and I don't really see him fitting anywhere else because he's so WTF to me, so having Jessie + Cait Sith seems improbable to me.