1) Being a Dungeon Effect spell and not an actual battle, the Power Word ignores monster attributes that would normally forbid you from attacking or defeating them.
Since Power Word: Kill uses the word "defeat," it cannot bypass traits that prevent a monster from being defeated. Traits are always on, and always checked. It can bypass Battle effects that prevent defeat, since those haven't been resolved yet.
2) All monster battle effects are resolved immediately after defeat by Power Word: Kill.
No, Battle effects are no used since a battle was never started. However, any traits that say "when defeated..." woudl still apply.