Activate by paying 1000 Life Points. Monsters that are banished, as well as monsters in the Graveyard, cannot activate their effects (that start a Chain).
Soul Drain has PSCT. If it doesn't say it negates stuff, it doesn't negate stuff.
It does stop cards from activating. Almost every Dark World effect activates in the graveyard, so it keeps them from activating. Wind-Up Rabbit activates on the field, so Soul Drain will not keep it from activating.