Re:LieF Spoiler

That island was a virtual reality construct created for the Tryment Plan.  The attempted murderer doppelganger is Tsukasa's original personality stabbing the surface personality that dominated in the other paths.  The wings were an expression of the master AI's (Alpha's/You's) administrator privileges.  Momo has access to Toto and her tablet as a virtual item because it would have been impossible to get her to believe the island was real without Toto.  Also, the other three paths were 'explained' as simulations done by the master AI as to what Tsukasa would do in various situations and the results of his actions.  The reason the doppelganger (Tsukasa's original personality) and the surface personality were actually able to completely separate for a time was because the surface personality was born of his fusion with the AI implanted in his brain after the accident.  In all the simulations, Tsukasa eventually dies, or so it is implied by the master AI and Ai herself.  That he was able to wake up in the true ending was the miracle born of him reconciling his past self with his current, partially artificial self.