I know others have already responded, but:
For me, it's more even than whether he's a robot; he's paranoid about what's inside him, which obviously intersects with his paranoia that he might be a robot. But it's the terror about not knowing what's inside us without cutting into ourselves.
Regarding Ava's actions at the end, I think this is fascinating. I taught this movie once, and my students loved it... until the ending. They wanted to sympathize with Ava, but said they couldn't when she abandoned Caleb to die. This betrays the implicit anthropocentrism with which we approach the film. We want Ava to accord with what we would expect a human to do--but why should she? She's a machine being held captive. I think my students' dislike of the ending also betrays our (and I'm using "our" very loosely and generally) failure to realize that Caleb is complicit in Ava's captivity, even if he falls for her, or whatever. He may want to help her escape, but Ava has no real reason to trust him. She's playing the long game; he's falling victim to his very human emotions.
When I taught the film, all except one student in the class was a man. When the men voiced their dislike and discomfort with the ending, the sole woman in the class expressed her confusion. She felt Ava was justified, and that her actions didn't constitute a betrayal or anything. This is to say, there's undoubtedly a gender analogy to the narrative, and it's nearly impossible that Garland is unconscious of this. Alan Turing actually lifted his version of the Turing Test from an older version in which two unknown players (one man, one woman) both try to convince a male observer that they're men. So from the get-go, the Turing Test is already a gendered construct. Ex Machina definitely plays off that.
