Plot hole: It makes absolutely no sense why the Terminator, who is a programmed killer, chooses not to kill anyone in this film. In Terminator 2, he didn't kill because John, who was his master, ordered him not to. In this film, we learn that John is not his master. Kate Brewster is. And she spends most of her time complaining and trying to escape from John and the Terminator. She certainly wasn't gonna bother giving the Terminator a pep talk on no killing. So it just remains a plot hole.
Suggested correction: Kate Brewster told the Terminator not to kill when she reprogrammed him in the future. It's a logical order to give since its mission is to protect. It's likely John gave her that idea in the future when telling her about the terminator from T-2 (before he died of course) who he gave the same order to.
I agree, but it is also possible that Kate programmed him not to kill anyone.
That's what I said.
Suggested correction: This isn't a plot hole. It's just your unfounded assumption. There's no evidence to support the supposition that the T-X has such audio detection capability.
Even if she could detect it, how could she discriminate between the sound of Catherine breathing and that of the dozens of caged animals in the room? That's stretching even fictional technology a little far.