Great topic! To my knowledge, there are three primary sources for information that may answer these questions. They are the Battletome, the Malign Portents story Dying Star, and Skaven Pestilins by Josh Reynalds.
How do the Seraphon contend with the end of the old world and their exodus from it? And how are the Seraphon thinking about the plan of the Old Ones now?
In Pestilins, there's a Starpriest that comments on this:
The skink eyed him. ‘The stars change. The skies burn. The war remains the same,’ it chirruped. It raised its claw in a complex gesture. ‘Always the war. Great Kurkori dreams always of war. The last war and the first.’ The skink straightened abruptly. Its head swivelled, gazing at its seemingly insensate master. ‘Never to wake, only to dream, until dream’s end.’ It turned back, fixing Zephacleas with a beady eye. ‘You are part of it?’
So from that Skink's perspective, the only thing that matters is the war against Chaos. Worlds may burn, but so long as Chaos remains, the war will continue.
A little later in the same story, we get what is to my knowledge the only Slann Point of View piece that exists in AoS:
The world was different, but the game remained the same. Sometimes Kurkori dreamed of the world-that-was, of humid greenery and a sky full of falling stars. He dreamed of the vermin, flowing up the wide, stone steps of ancient temples in their chittering hordes. He dreamed of dead kin, eaten as they slumbered, their wisdom devoured by scuttling shadows. Anger filled him, and the saurus marching alongside his palanquin stiffened, growling. He heard the rumbling voice of his favoured general, Oxtl-Kor.
This matches well with what the Battletome states about when Dracothion encountered the Slann:
Tales tell of how during the Age of Myth the Great Drake, Dracothion, came to guide the seraphon to the Mortal Realms. From across the gulf of eternity, Dracothion beheld the glittering vessels of the seraphon as they drifted like motes of dust through the darkness. Overcome with curiosity for these strange alien objects, he sought them out. When the star drake drew closer, he sensed the minds of the slann, and within their thoughts a heady mixture of loss and rage.
So the Slann certainly remember the destruction of the World That Was, and they're not happy about it. Exactly how they contend with it is unknown, but summoning vast armies empowered by celestial magic to slaughter Chaos tainted creatures is probably quite cathartic.
As to the Great Plan, it seems each Slann has their own vision of what exactly that is. From Pestilins:
Great Lord Kurkori, the Dreaming Seer of the Second Departure, stirred reluctantly on his palanquin. His dreams held tight to his vast consciousness, drawing him into better and brighter worlds than the broken, limping thing he now found himself in.
In his deep dreaming, he saw an empire of order and light, a thing of perfect structure and harsh angles. The universe would move in perfect harmony, every realm, every inhabitant perfectly synchronised and in rhythm with the cosmic plan. It was a good dream, and one he intended to see made real, whatever the cost.
And a little later, in the same passage:
Chaos had grown powerful during the centuries of blood, but so too had his kind. The Dark Gods had learnt little with the waxing of their might – they were feckless abstractions, impatient and impulsive. Disharmony and disunity were their lot, and all things unravelled at their touch. They did not see the Mortal Realms for what they were, only what they wished them to be, and so were blind to the true nature of the game being played.
That they did this in isolation, each slann pursuing their own campaigns against the slow advance of entropy which threatened to consume eternity, did not hamper them at all. For all that they were the merest fragments of a long extinct civilization, the lingering debris of a vanished world, they were not without some power.
The Eight Realms were a great game board and the Starmasters placed their pieces with calculated precision. They saw many moves ahead of their inattentive foes, and wove iron-hard stratagems which would advance their singular cause, however infinitesimally, from a thousand different angles. Step by step, Kurkori and his brethren manipulated the winds of fate with their celestial mathematics to bring about the final defeat of the ancient enemy.
And from the Battletome:
To the slann, the Mortal Realms are a great game board upon which the armies of Chaos will be fought and defeated. Placing each piece with
precision, they are able to look many moves ahead of their enemy, engaging them in battle when and where they choose. Step by step, they manipulate fate to bring about the final defeat of Chaos.
Despite this unity of purpose, the seraphon are also a divided race. Each slann, and the cohorts of warriors they summon, is but a fragment of a long dead civilisation, and each has their own view of how the war for the Mortal Realms should be waged. The slann will often endure millennia of solitude, only rarely connecting with their kin. In this time, each individual slann pursues their own campaign against the servants of Chaos or those that would stand in the way of perfect order for the realms.
When many slann gather for war it heralds a truly momentous battle – the stars themselves move into alignment, promising the destruction of empires. In such instances the seraphon are at their strongest, their celestial might almost unrivalled.
So overall, it seems the Slann each have their own vision for the Great Plan, but there's some unity of purpose. They all desire the destruction of Chaos, but in its place they see a world of perfect Order (which it's worth noting would quite probably be an extremely unpleasant place to live). How to best bring about the destruction of Chaos is something the Slann disagree on, and is a potential source of conflict.
Are any of the non-Slann (assuming your fluff treats them as separate entities) starting to question the Slann given the state of things?
In Pestilins, there's a number of PoV parts from non-Slann. First is an Old Blood:
Irritated by the smells and sounds, Oxtl-Kor rubbed his snout. He was covered in a latticework of scars, each one a page in his history since the final beginning and the first ending. Sometimes, in the red moments between the his master’s call and the triumphal dissolution which saw him returned to the calm and quiet of Azyr, the Oldblood wondered where he had gained them all. It seemed to him that he’d had some for longer than he had been alive.
There were scars on his mind as well as his body. Gaps in his memory, where his thoughts grew thin and faded, and when he became frustrated by them, only the death of his foes could sate him. The Oldblood longed to deal death to the vermin, to feel their flesh tear between his jaws, the hot rush of their blood sliding down his throat. That was his part in the Great Lord’s dream. He was the savage longing of his master made flesh. He was Kurkori’s rage, and he was content only when killing. Sawtooth grumbled in seeming agreement, and Oxtl-Kor patted the carnosaur’s thick neck.
Then, the Starpriest from before:
Takatakk cocked his head. ‘Great Lord Kurkori says–’
‘I know what he says, Starpriest,’ the Oldblood rumbled. He tapped his skull with a claw. ‘I hear his words in my blood as well as you. I will not fail. The stink of the vermin-spoor is strong, and Sawtooth’s belly is empty.’ He looked at their master, reclining on his throne. ‘His wishes are many, and all must be fulfilled, even the least of them. I follow the Dreaming Seer’s design, even as you do.’
The skink grunted. He clicked his jaw, uncertain. The plan stretched before him, but even he was not aware of every facet of its infinite complexity. He was but a conduit for the wisdom of his master, an extension of the Dreaming Seer’s will. To him fell the mundane responsibilities of battle, the guiding of the unruly along the predestined path. Oxtl-Kor was more unruly than some. ‘We will march for the great worm’s head. You must mark our path, O veteran of wars yet undreamt. Show us their trail,’ he chirped.
Then, a Sunblood:
The Sunblood swung his head about, studying the ebb and flow of the enemy tide. He could perceive a foe’s weakness as another might scent the blood of a wounded animal. Spotting the weak link in the swarm of skaven, he roared. Instinctively, the nearby seraphon lunged forward. They fell upon the skaven with a savage joy that was a match for his own. They all remembered, and in remembering, felt the old hate rise anew.
But they were not alone in that hate. Sutok glanced down at the armoured figures fighting alongside him. Yes, they were not alone. It was good not to be alone. Oxtl-Kor did not understand that. Sutok felt no sadness at the Oldblood’s death. It was the thing of but a moment. Sutok himself had fought and died a thousand times, and each of those deaths was but a moment experienced and then forgotten.
It was a good thing, to be a dream.
From Dying Star, we get the perspective of a Starpriest:
The Starpriest eventually came to a vast, spherical cavern with a single bridge of gleaming tiles leading across empty space. As he walked, Maq’uat peered down to the floor of the World Chamber, leagues below. There lay a great expanse of jungle, gouged by glittering river deltas. He felt a tinge of longing. It had been too long since he had hunted with his spawn-kin, since he had smelled the sweet scent of swamp air and felt the warmth of sun-baked rock under his skin. But that was all a distant dream. His master needed him, and Maq’uat would serve Lord Xuatamos until lonely death if it were asked of him.
So from all this, we can see that the Seraphon are absolutely united behind the Slann. Certainly none of them seem to question the Slann's plan, regardless of what happens, and if dying is required, they're either accepting of it or, in the case of the Sunblood in Pestilins, quite happy since he knows he'll come back over and over again to fight.
Are the surviving Slann more united than before? Or are they even more fractured and disparate in their motivations?
As the quotes above show, the Slann are far more fractured. Dying Star seems to indicate that each Temple Ship is controlled by a single Slann, meaning that each one has a degree of tremendous autonomy. They can operate entirely independently seeing as each has a ship which gives them everything they need to wage war. They almost never meet up, which is hardly surprising given they're either always on their ships or in the Realms with an army around them.
If you consider the Skinks and Saurus as memory constructs (temporary or otherwise), is their psychology impacted by the Slann who thought them into existence?
The quotes above seem to give this some support. The Starpriests certainly mirror their Slann's thoughts, and the Slann in Pestilins talks about the various Seraphon he summoned being aspects of his dreams and emotions:
He could feel the pulse of star-born energies that were his chosen cohorts. Each one was as unique as the stars in the firmament, and as precious to him. They were his claws, his fangs, his darkest dreams made scaly flesh. When they roared, they roared with his voice; when they bled, they bled with his blood. They were his dreams, and he wielded them with a deftness that was spoken of in awe by his fellow slann.
The central points of his constellation glowed the brightest – his rage, his cunning, his hope, made manifest in his chosen champions. Oxtl-Kor, a proud beacon of cold fury and determination; Takatakk, a quicksilver flickering of celestial power, ebbing and strengthening with Kurkori’s attentions; and Sutok, saturated with the very stuff of Azyr, his scales glowing with the light of the stars themselves.
Some of the Seraphon, like the Sunblood Sutok in Pestilins, certainly have been altered by their changed existence. He loves being a dream because it means he can fight forever regardless of whether he dies or not. Whether that's affected by his Slann or not isn't clear. It may be that all Sunbloods feel this way.