What could explain a lot is if the Fake Red is really Katarina in drag (or after sex change surgery)... surely would explain why she loves Liz and would do anything for her... and the whole thing about the old guy in the woods and why he cant stand the fact that this his 'daughter' Katarina is now a 'man'... and the other old guy who was killed in the bed by the Fake Red with the pillow... and two episodes which make much more sense under this premise is the one 'out of the ordinary' episode where Fake Red 'finds' Katarina in some old beach house/resort near the beach and ends up watching Katarina walk out into the water.. how many 'psycho' thrillers have you seen where a mentally ill person (crazy) if you will has these sort of 'day dreams'... and the other episode Mr Kaplan was 'found' by Katarina and only dealt with Katarina when she had Liz around as a baby... would explain why she was suddenly so 'into' Fake Red..
Of course, this is just speculation.. though it certainly does answer some questions :)
