When the Architect says Zion is dead, how is that true?

This would need to be a lot longer to answer all of your questions. I suggest following the links below to gain a more complete understanding.

As explained here, the Architect acknowledges to Neo that he failed multiple times in creating a Matrix that 100% of humans accepted. The current "successful" Matrix we find Neo in is only accepted by 99% of humans. The remaining 1% are the rebels found in Zion, trying to defeat the machines.

The problem is, since the Zion-crew are constantly trying to unplug humans from The Matrix, that percentage will grow and cause a system crash. To create a balance against that eventuality, the Architect designed the current Matrix to have the Oracle, who would reveal The Prophecy to the defectors and send them on the wild goose chase of finding The One who would (hopefully) destroy the machines and free mankind from The Matrix. And to quote from the link above,

Behind this door the current version of Zion is destroyed, but the One selects 23 people to build the next version. Humanity lives on in a cycle of controlled futility as the machines allow them their 'rebellion'.

All 5 of Neo's predecessors chose that door, rebooting The Matrix (resulting in the destruction of Zion) and starting over. This kept the cycle going, which kept the 99% of humans oblivious to the fact that they are essentially the batteries keeping the machines up-and-running.

The point of the movies, found here, is that because of The Oracle's well-laid plan, Neo chooses the other door. The outcome is that the machines make a deal with Neo to stop the destruction of Zion and allow the 1% to live outside of The Matrix going forward as long as Neo can destroy Agent Smith (the new true threat to both humans and machines; See subsection: The Oracle's Gamble from second link).

To quote the second link:

Neo allows the inevitable to happen, unbalancing the equation, thereby giving the machines control of Smith through Neo's jacked in body. Neo-Smith is destroyed by the machines, then all the other Smiths are destroyed, leaving programs he previously took over lying on asphalt, 'free' again. Smith is defeated, and the Matrix reloads to version 7, with Zion persisting this time.

And from the FAQ page on that site to provide further explanation:

Smith has taken over Neo, fulfilling his only purpose, and unbalancing the equation. He's also directly connected to the machine mainframe through Neo's body. The machines can now delete him and revert/delete all his copies. Neo's body is carted away by the machines to assimilate his code into the mainframe. There is now a fragile peace between humans and machines. The machines, through the Architect, agree that minds that want to be freed will be. Zion will persist, with all their memories of what has happened. Humanity will begin to rebuild, freeing minds from the Matrix in manageable numbers.

And to support that, in the last scene in The Matrix Revolutions, we see The Architect speaking to The Oracle about the dangerous game she played. She responds that, "Change always is." The cycle has been broken, and Zion is spared.

The Architect is being literal. He has wiped out the population of Zion before, and is poised to do it again. He explains to Neo that the purpose of The One is to perpetuate the cycle. To that end, Neo is expected to select a number of people from the Matrix to free, and is told that they will become the foundations of the next Zion.

The Architect: The function of the One is now to return to the Source, allowing a temporary dissemination of the code you carry, reinserting the Prime program, after which you will be required to select from the Matrix 23 individuals - 16 female, 7 male - to rebuild Zion. Failure to comply with this process will result in a cataclysmic system crash, killing everyone connected to the Matrix, which coupled with the extermination of Zion will ultimately result in the extinction of the entire human race.

So this batch of Matrix refugees will be destroyed, but a new group will be freed and brought by "The One" to this underground haven, no doubt explained to them as a remnant of the war -- indeed, the scars from the battle will still be evident -- and given their mission to seek out others in the Matrix that are capable of expanding their minds sufficiently to be unplugged. He gives them everything they need to begin, and then promises his eventual return to give them hope and a salvation for their labors.

This mirrors Morpheus' explanation for how the story of his Zion was founded. "It was he who freed the first of us," he tells Neo, pointing to a time when Zion was empty and a small band of rescues were brought there by someone who wielded great power over the Matrix.

Zion is in the Matrix. That is why Neo has powers to destroy the machines on the way to the machine city. Also Neo is actually in hell, he is a criminal, and he wakes up in a hell hole... literally... with lava flowing around them during their little celebrations in Zion. He accepted (FALSE) "Trinity" and Morpheous as his saviours, when in fact they are criminals. They lead him astray. Like it or not... the majority of the population is Christian, and people love to mix Christianity into their works as it works as at a subconscious level.