Kyle's ability

She could be a ghost. The dead my have access to all manner of insight and foresight. Or it could just being able to see into the spirit realm like Native American shamans.

Or maybe, Kyle's ability is to be some sort of living computational computer, like John Nash (A Beautiful Mind), with the ability to divine future events by subconsciously computing all known variables at insane speeds in his mind, to their logical conclusions are derived. But like Nash, Kyle's ability has driven him down the path of insanity, where he creates imaginary people (or an imaginary alter ego) in his mind to help him cope with the computations his mind is doing and to understand them in real world terms.

Or maybe his ability is direct communication to one person (Cassie) from somewhere in the future, who's ability in turn is direct communication with one person (Kyle) from somewhere in her past. Think of it as some sort of psychic Corsican Twin  (Crimson Guard commander Tomax & Xamot) like bound. But instead of across distance, the bond is across time.