Selina Kyle's importance I believe that Nolan went with adding Catwoman/Selina Kyle to the movie as a way to help Bruce out of the darkness he has put himself into. After becoming injured while trying to save Gordon's son from Harvey Dent, Bruce lives away from society. This is because he cannot see a life outside of being Batman, which he has since given up; his only motivation to put away his Batman persona was to be with Rachel, and since her death, he lacks the drive to move forward. This becomes aparent in the conversation Bruce has with Alfred after Bruce investigates Selina Kyle in the Batcave.
In interviews I recall from the Blu Ray in the "A Girl's Gotta Eat" segment, Bale and Nolan comment that Selina one of the few people who Bruce does not feel he needs to put on a mask for. She does not find him intimidating as the rich and mysterious recluse Bruce Wayne, and is not afraid of him while he is Batman. Bale himself says in the segment that Bruce finds her "amusing", and Bruce feels comfortable enough to view her as an equal to himself.
Her importance to Bruce and their developing relationship may also play into the final scenes of the movie. Prior to being put into the prison by Bane, Bruce did not fear death. Once he realizes that he has to be, this drive helps him to make the jump to climb out of the pit. This fear of death also plays into why he is not able to die with the reactor, and instead fix the autopiolt, and in the end, be with Selina. Although it is only speculation, I think it can be fair to say that one of the reasons he had to live was to be with her.
In conclusion, Nolan added Selina as a character that would give Bruce the drive needed to not only become Batman again in order to later save Gotham, but also the female equal he longs for that will give him a will to live.