During the Architect scene, the room is filled with screens showing Neo as he is within the room, speaking to the Architect. These screens can also be seen in the first film, showing Neo before he gets interrogated by Smith. What I am wondering is why Neo changes his responses from screen to screen, does this mean that no matter what the Architect sees, he doesn't see the correct answer unless the answer is directly in front of him?
Based on what we see in the film script, the monitors appear to represent what The Architect anticipates will be Neo's reaction/s to his revelation about the true nature of the Matrix, Zion and the role of The One. As Neo's actions resolve, the other potential lines of thought are closed off.
Note that the script explicitly calls these out as all being the same Neo and not previous "The One"'s that may have come before him.
ARCHITECT (CONT'D) The Matrix is older than you know. I prefer counting from the emergence of one integral anomaly to the emergence of the next, in which case, this is the sixth version.
[The Neos respond in a barrage.]
Neo: There were five Ones before me!
Neo: That's impossible. It doesn't make sense.
Neo: You're lying. This is bullshit.
Neo: I'm afraid.
Neo: If that's true...
Neo: How could that be?
Neo: There are only two possible explanations...
[We move towards a specific Neo, centered among the others, closing in on a single line of thought.]
Neo (Cont’d): … Either no one told me, or no one knows
TL;DR: The screens show the possible paths Neo can take and Architect calculates all possibilities.
Architect's primary function is to balance equations. In order to do so, he needs to calculate every possible response Neo might give.
Note that when Neo decides to ask a new question, the camera converges to one of the screens and they continue from that screen. When Neo decides on something, the possibilities are narrowed to that decision alone. I haven't watched director's cut, but this scene had always reminded me of quantum measurement and consequent collapse of the wave function.
Contrary to what you suggested, Architect did not know Neo's answer right away. He did sense that his love is concentrated on Trinity beforehand, but he obtained the definitive answer looking at the chain reactions and chemicals in Neo's body, or code, after he revealed that Trinity is going to die.
As the Architect explains, the Matrix has crashed before. Neo (Greek for new) is a failsafe routine, an attempt to forestall future crashes by stabilizing subroutines that exceed their restrictions. Unlike other routines, he has the ability to reprogram himself, that is, he has free will.
The screens in the Architect's room show the previous meetings with Neo. They vary slightly, but they generally show Neo becoming angry, for the same reason he becomes angry in the present--he feels he's been manipulated. Each screen is from a different incarnation. The room is one of the most secure places in the Matrix, and it has data from previous versions that isn't available elsewhere. The Architect claims that Neo has been there five times before, but there are many more than five screens. It's possible that the Architect, like any routine, has biased, limited, or incorrect information, or that he too is malfunctioning.
The reason for the screens is less clear. The original Architect (we only see his avatar here) may have felt that Neo would learn from previous mistakes. He may have felt that, as an egotist himself, Neo too would respond to his own image. More likely, the Wachowskis felt it made a cool visual.
Other interpretations, of course, are possible.