The very last puzzle seems unsolvable until you realise that you can use Ava's body in the same way as you could use any other inanimate object, by letting it go around on a moving band to intermittently block a beam, while you use a robot to go solve the puzzle. In other words, to complete the game, you need to symbolically accept what you've already technically known since halfway through it - that not only are you not playing as Ava, but that Ava is a tool being used by TOM (your actual player character), functionally no different from any of the cameras, robots and guns that he can also "jump into."
Didn't think of this solution, solved it another way: by kicking the block and switching agency to a robot before the block lands on a button.
The title, aside from being a play on the fact our main protagonist is named Turing, and the obvious name drop of the classical Turing test, is also entirely the point of the game- it's just that you expect it to be a case of "Human needing to determine if a Machine is human, when the problem of the game is just the opposite- TOM has issues believing Humans aren't machines. Why not? After all, humans are victims of causality and following their own instinctual impulses more than any any logic. That and He has complete control of the crew, including Ava, and can adjust their moods and impulses. He even outright states that humans don't have free will even without him controlling them. The climactic encounter at the end is essentially both parties being subject to a Turing test and deciding the other is a machine- TOM believes himself to be more "Human" due to his control and logic and sees the rebelling humans as "faulty" and thus valid to kill, while Ava and the others see Tom as a heartless machine rigidly following flawed orders and thus see no problems shutting him down. Your decision at the end is which party you feel is "human". Either ending has some regret, as in one you decide on party isn't, and you suffer guilt for it, or you don't, but due to your previous actions, it's not enough to convince them that you're human or trustworthy.
A TOM that could kill Ava and override its do not kill humans programming is very human indeed, especially if it can feel guilty over it, but a TOM that can't bring itself to kill Ava even with the fate of Earth at stake is equally human...but would be construed as "TOM following his programming to not kill humans" and thus nothing more than a machine to Ava and the others. So the deck was somewhat stacked against Tom in this scenario...
At one point, when Ava asks TOM for a hypothetical solution to one of the puzzles, he suggests chopping off her arm to hold down a weight-controlled switch so it stays in the "on" position. If she chopped off her right arm that would have severed his connection with her.
How in hell did five people manage to construct such a vast Elaborate Underground Base from nothing but modular storage compartments, not to mention while basically on the run from the AI that controls the entire facility they were redecorating? Where did all that tech come from? Why did they even have enough space available in the first place? Many of these rooms are massive, after all. Frankly, the more you think about the backstory, the less sense it makes.
Well, it's not even much "fridge" that many game statements make no sense. We have a virus which "repairs DNA by taking DNA of other organisms" (a close analogy would be to repair a book by tearing pages out of random other books), pavlovian conditioning in regards to very complex and subtle behavior, outright hysterical behavior of Sarah on logs in which Ava sees nothing wrong, a completely butchered explanation of Chinese Room experiment (one would expect that at least someone on the crew knew the word "qualia")...
