First off, she said she's waiting for her turn, not to turn. There's a difference. One specifically means she is waiting until she becomes an infected. The other means that she is waiting for her turn to die, as (almost) all her friends have, and it should rightfully be her turn by now.
She's not going to change, the recorders in the Hospital made that clear.
Ellie's immunity is due to the fact that the cordyceps stopped at her brainstem when it mutated there. As for why it mutated, and how, we won't ever have an answer. It could very well be that there are other possible immune candidates out there, as the doctor noted nothing special about Ellie from his quick examination.
The answer is unknown as to whether Ellie's bite can infect someone. Yes, she told David such when she bit him, but every instinct in me (and many others) says that she was lying as a distraction. Now, that's lying on two fronts. The first lie to David so that she could get away, and the second lie to herself, because she does not actually know either. We can all hope that the DLC somehow shows this, but I sincerely doubt it.
I doubt that Ellie's behavior has been altered by the cordycep, and I also seriously hope not. I won't want to play through a DLC in which Ellie is passive. I'm now suddenly worried that they will do this so that we play as Riley.