Firstly - kills. Yes. My pokeball theory is that when a pokemon in a pokeball is taken to a pokemon centre, it can be re-healed to a previous stage - much like a computer's backup - even if it's dead. The dying and reviving creates a connection between them - they're alike in that regard.
Doom desire - i do have a reason for that. Asbol's pokedex entry states that it causes (or predicts in some cases) disasters. My fictional theory is that an absol enters a cursed state while asleep, and casts doom desire upon an individual - or a town - which is nearby.
Celebi... okay, i'll have to think around that. That's a good point...
Thanks for the help, btw.