Fridge Brilliance can explain Shizuru's Psycho Lesbian phase. She doesn't become unhinged until after Nagi informs them all of the true nature of the Festival. Shizuru is pretty sharp. Her MIP is a HiME, as was she. She knew there was no way she could win. If she lost, Natsuki would vanish. If Natsuki lost, her MIP would vanish. Shizuru didn't know who Natsuki's MIP was, and given some of her statements, she had no reason to believe that it was herself. But she knew that if Natsuki lost, she would be deeply hurt by it. She was backed into a corner, and couldn't see a way out. Even suicide was out because Nagi had informed them all that killing yourself would instantly cause the death of your MIP.
In the Drama CD track "As the Cherry Blossoms Bloom," this is confirmed when it is revealed that Nagi approached her individually at some point after Episode 16, told her about the fate of the Himes, and said that she won't be able to hide any longer "because (her) beloved Natsuki-chan is not going to be able to escape this fate, either." Shizuru then realizes that her losing will cause Natsuki to vanish, but then wonders if Natsuki will one day accept her feelings.
So it makes sense for Shizuru to go insane when Nagi—who doesn't have the greatest track record for telling the truth to begin with, as a "sharp" person should easily notice—makes unfounded verbal threats, even though she didn't give a crap about Natsuki and managed to act completely rationally back when Alyssa was actually about to kill her with a proven Kill Sat? How does that even remotely work?
Shizuru's supposedly raping Natsuki being left ambiguous, with even the writers refusing to confirm or deny it, seems like a bit of a cop-out. But then you consider that the most relevant issue, from a story perspective, is not whether it happened, but that Natsuki, at least for a moment, thinks that it happened. The entire situation came about in large part because Natsuki lost her powers from hearing that her mother was planning to sell her to the Searrs Foundation, and the idea that Natsuki could have been betrayed by someone so dear to her shakes her to the core. The mere idea of Shizuru doing something similar to Natsuki by raping her in her sleep would have a similar effect on her. In the end, however, Natsuki decides to trust "the mother (in her) heart", rather than question what was said about was true, and it is likely for similar reasons that she chose to forgive Shizuru. It also complements Natsuki's character development, going from someone who couldn't trust anyone, to learning to trust others only to have that trust possibly broken, to someone who once again trusts people close to her.
According to Japanese mythology, Japanese nobles are descended from dragons, who instinctively know their soulmates. Once they have met and been accepted by their chosen mate, their physical and mental health depends on the continued presence of their mate. Fujino Shizuru is probably of noble blood, if her skill in the traditional arts is anything to go by. Met Natsuki, had issues remembering that other people mattered, but was kept relatively stable by Natsuki's presence. Note that she didn't snap until she was blatantly rejected by Natsuki, and was brought back to sanity by same's acceptance. Diagnosis: Her Inner Dragon was bashing its head against the wall.