He does not 'discuss' anything with Nagini lol. Nagini is a snake with the brain of one and she cannot have intelligent discussions. He is merely thinking out loud, as he often does.
This anon is so desperate to make them closer than they actually were. Snape delivered a prophecy that Voldemort thought was life-saving, and he didn't even need to do it. He voluntarily did it! He wasn't tasked or anything. The least Voldemort could have done was to try to spare Lily, who was a Muggleborn, yes, but also very young and not particularly important. It would have cost him nothing to spare her, and he still killed her! He didn't keep his word. He could have stunned her but his promise to Snape (who had saved his life, remember?) mattered so little to him he still killed her for no reason at all.
Do they not realise how demotivating it would be for a Death Eater to deliver something so significant involuntarily and for the Dark Lord to not even fulfill a simple request? Voldemort always talks about how he rewards his followers but he humoured Snape, nothing more. The fact that he agreed to spare Lily for about five seconds before killing her anyway just shows how meaningless Snape's plea was to him.
Snape gave Voldemort something extraordinary and he did it voluntarily, devotion on a silver platter! Snape's one request, the smallest, most impersonal request imaginable, was ignored. Voldemort couldn't even keep a simple promise that would have cost him nothing, and to someone like Snape, who was already rejected and humiliated by everyone and found belonging among the Death Eaters, that moment would have been shattering. It would have made him realise he didn't belong there either. He must have realised, right then, that he could pour his soul into serving Voldemort, risk everything, and still be discarded like rubbish, and he was right.
Years later, at his death, Voldemort does it again. In his eyes, Snape spent decades collecting information and proving more useful than every other Death Eater, but he still kills him for the Elder Wand despite knowing murder wasn't necessary to win its allegiance. He knew Dumbledore won it without ever killing Grindelwald, but he still kills Snape on a whim, not even trying to spare him, and why?
it seemed more prudent to finish them all.
we never really see him act this way with other DE's
He rescued Bellatrix from the Ministry and squandered two years of careful planning to remain secret, for no reason but to save her from temporary imprisonment even though he didn't need her for anything until he freed everyone else who was captured. Not to mention that the Dementors were under his control at that time and he deliberately prolonged rescuing everyone else, probably just to punish them. What made Bellatrix so special that Voldemort didn't lift a finger to grant Snape's request for sparing Lily, a tiny, harmless mercy after he delivered a lifesaving prophecy, but destroyed two years of planning to rescue one woman?
Why does nobody ever question Voldemort's murder of Snape when he knew Dumbledore didn't have to kill Grindelwald to win the wand? Voldemort knew Grindelwald was once the master of the Elder Wand. He knew Dumbledore defeated him and locked him in a prison. He was also fully aware that the Wand was now Dumbledore's. Voldemort never thought murder was the only way to win the allegiance of the Elder Wand and he had two expert wandmakers as his prisoners who would have confirmed this.
Voldemort knew he didn't need to kill Snape to win the allegiance of the Elder Wand but he did it anyway because he never trusted him. This thread is woven subtly but intricately through the books. Even after he killed Dumbledore, Voldemort used Legilimency on Snape when he was giving him information:
'Saturday... at nightfall, repeated Voldemort. His red eyes fastened upon Snape's black ones with such intensity that some of the watchers looked away, apparently fearful that they themselves would be scorched by the ferocity of the gaze. Snape, however, looked calmly back into Voldemort's face and, after a moment or two, Voldemort's lipless mouth curved into something like a smile.
Bellatrix in Spinner's End had information that only Voldemort, Snape, and Harry knew (the Philosopher's Stone and Snape becoming an obstacle) as LV didn't mention it in the graveyard, which clearly indicates they had a discussion about him where he shared his mistrust of him with her but they both reached different conclusions. Since Bellatrix escaped Azkaban six months after Snape rejoined Voldemort, it's obvious he was still not sure of his loyalty.
'A hundred reasons!" she said loudly, striding out from behind the sofa to slam her glass upon the table. Where to start! Where were you when the Dark Lord fell? Why did you never make any attempt to find him when he vanished? What have you been doing all these years that you've lived in Dumbledore's pocket? Why did you stop the Dark Lord procuring the Philosopher's Stone? Why did you not return at once when the Dark Lord was reborn? Where were you a few weeks ago, when we battled to retrieve the prophecy for the Dark Lord? And why, Snape, is Harry Potter still alive, when you have had him at your mercy for five years?'
LV also sent Wormtail to Snape's house, who according to Snape liked to eavesdrop all the time. He was clearly sent as a spy by Voldemort to keep an eye on Snape.
'Really? I was under the impression that the Dark Lord placed you here to assist me.
'My apologies, said Snape. 'He has lately taken to listening at doors, I don't know what he means by it... you were saying, Narcissa?'
Voldemort clearly saw the Elder Wand as an opportunity to finally get rid of Snape. He even told him that although he is talented, he is no longer that valuable to him.
my Lord, their resistance is crumbling -'
- and it is doing so without your help, said Voldemort, in his high, clear voice. 'Skilled wizard though you are, Severus, I do not think you will make much difference now. We are almost there... almost.'
He was seeing it as a gamble from the start. Snape, if truly loyal, could prove very valuable and useful to Voldemort with his talents and inside information. Yet, if not (i.e canon) he could risk a lot, but he probably underestimated the damage Snape could cause if he wasn't loyal.
There's also a very strange claim going around, usually perpetrated by some Snape fans, that Voldemort was fond of Snape when the books never imply such a thing. His murder of Snape leaves that completely unambiguous.
'I regret it,' said Voldemort coldly.
He turned away; there was no sadness in him, no remorse. It was time to leave this shack and take charge, with a wand that would now do his full bidding. He pointed it at the starry cage holding the snake, which drifted upwards, off Snape, who fell sideways on to the floor, blood gushing from the wounds in his neck. Voldemort swept from the room without a backwards glance, and the great serpent floated after him in its huge protective sphere.
He's really twisting the knife here with the cold 'I regret it', followed immediately by his own declaration of his true feelings in his own mind: there was no sadness in him, no remorse.
Useful was all Snape ever was to Voldemort, and when that usefulness ended, so did Snape's life.