Battler wasn't actually trying to "get the right answer" so much as "get any answer that doesn't require magic", so the kind of thinking we do in this thread isn't actually required of him. I wouldn't blame the guy.
Anyway, as far as Natsuhi in EP1 goes, I'm convinced she has split personalities (the other being convinced she's Beatrice).
http://en.wikipedia.org/wiki/Dissoci...ntity_disorder
Maybe it's a matter of the symptoms just conveniently fitting the situation, but that incurable headache and that weird feeling she gets when she wakes up? It'd also explain why there's blood on her door. She may have then washed her hands when she got inside.
Anyway, as far as 4's Kinzo sighting...