what would that make the parallel Neo's that the Architect shows him?
Think about video games. Two dimensions and side scrolling, yeah? Then a third axis is added to simulate depth. Tetris: blocks fall from the top and move left or right. What about forward and backward? When you see the screens of Neo, you are seeing the dimensions or sides of Neo at that moment as seen by the matrix. At first, the emotions are scattered and indicating a cluster of emotions but then they begin to harmonize before becoming a clear feeling that Neo registers.
Thus, the Architect explains how precursors in Neo's mind work to shape and formulate; he's telling you and Neo that the matrix is reading as surely as it is writing.
I would say that a typical iteration would end at the conclusion of the Neo-Savior plot-line, and restart at some arbitrary beginning to the modern era that the robots would set
Perfectly reasonable here. Story goes the 'one' returns to the source patching the matrix and selecting people to run Zion. A handful of people carve a life under ground with techno and porridge. They exist with an understanding that one day machines will overrun the city unless a savior appears. On that day, only a few will live whilst the matrix is patched and the process renews. By the next one, those chosen by the previous 'one' are long dead. Otherwise they'd be talking about the last time the matrix was patched. Each iteration, then, spans a few lifetimes. Enough time to populate hovercraft with competent crews and fortify Zion with mech units and a slick operations center.
Maybe Neo does learn and adapt over time through iterations, and that is an interesting different speculation, though there seem to be too many of those parallel (being interpreted as past) Neo's for him to have just lived through the plot-line that many times repeatedly, being reset at the start after his struggle in the Matrix, and they seem to similar to Neo to be his ancestors, they're all Keanu
The 'one' is a moniker like 'Neo'. You could reason that Keanu has appeared each time with a different hacker handle but the same moniker - 'the one'. Still, why in the iteration we see does Neo care so deeply for Trinity when obviously the past has been different. Assuming it's always Keanu then it's also always Morpheus and Trinity. Why the departure of its always the same people?
It isn't the same at all. You can measure time according to matrix iterations, generations grown in Zion, or by the time taken to build up the technology at Zion. However you measure time, there's only one Neo.
The Architect believes a certain irrationality is behind matrix rejection; he certainly believed his first iteration was marvelous, though widely rejected. In improving acceptance rates, the Oracle proposes a sort of gambit that accounts for the rejection rates as big bounties. At some point, a person inside the matrix will learn enough exploits to cause a cataclysmic failure. The machines recognize multiple people will learn to bend spoons but one in particular will always stand apart and lead the rest. That is 'the one' the machines target. That person possesses knowledge and the machines want to bake that into the source. Trouble is that 'the one' exits the matrix first, then presents to the machines. A honeypot is needed to bring the 'one' back to the source. In this way, the 'one' is updating the matrix when they die. Once the 'one' returns to the source, none of the previous exploits work. A more resilient matrix is loaded and Zion is seeded by the one as compensation.
Why?
The machines cannot account for the systemic anomaly. There's something about humanity that mathematics cannot capture in complete resolution. That's how previous 'one' entities had been used to balance the equation. The mind of the 'one' illuminates aspects of humanity that machines cannot compute. But Neo, first of his name, is different. The status quo is gone and the Architect sees it in Neo.
Neo isn't the systemic anomaly that rejects the simulation and then patches it; he's the one that rejects the Architect's offer and refractors the Oracle's solution. Up to Neo, every 'one' decided in the room with the Architect to accept the premise and dichotomy, save mankind and Zion by sacrificing themselves for the greater good. Neo left. That's new. Also, he hacks the matrix in ways no other has. The machines know what's up and they formulate a plan for existence without humans. That's a serious response. It only makes sense of the machines believe Neo could end their existence. The pitch in the room of monitors never hints that humans ever stand a chance of winning. This time they do.
It is philosophical but Neo cannot be the same person as previous 'ones'. The solution to that problem is too easily solved. Map the genome and terminate all humans that resemble it. No, the one is different each time. The human mind cannot be completely mapped by the machines so there are anomalies from time to time. Neo, however, is physically different and it causes him to think and behave unpredictably in the consciousness of the machines. Even if they solved for his mind, his nervous system is different and that means machines will need to change how they interface with humans.
When Neo drops the flying squid I think we are supposed to realize Neo really is different ... and so things aren't going to be anything like they've been before. That's exactly how things end, too. The disruption is permanent and better inclusive of will. Cipher-types can eat fake steak and Dozer types can eat amino snot.