Re: part 3 Snape has spent quite a bit of time in your story trying to teach her. By now, she should be doing more than repeating quotes from The Art of War at him. In the middle of the chapter, Snape challenges her to consider the ramifications of her actions. He also gets a dig in (quite rightly, IMO) about her self-righteousness and double-standards. She responds by demonstrating that she's not going to *think* about it.
They are teasing each other! He's constantly slinging these Art of War qoes at her, for once she beats him with his own weapons. And my Severus in that story has humour enough to see that and be amused. We do know that he has humour. He can even be self-ironic, although that is very hard to find in canon. But here, it's their way of flirting. And if she didn't ever reflect on things, why would she be worried about using Unforgiveables?
But he's been kicked around enough by now to have learned better than to waste much of his energy on a Granger who is not willing, able, or both to learn, think about the consequences of her decisions, and take the rap for them when they hit.
You really hate her. You don't even know where the story will go and just assume that she'll never learn. We probably have different ideas of what she needs to learn. Methods used when fighting (and she's been fighting powerful adversaries for a long time, without much help from the adults) are questionable. Wars aren't fought morally. The question is where you draw the line. Hermione struggles with that. Yet, you accuse her of never learning reflection, when Severus uses Imperio on Trelawney because it's convenient. With a bit of reflection, he surely could have come up with another solution.
Hermione's plan never required to use an Unforgiveable. Severus chose it as an extra precaution, and he never mentioned it to her (because I am a lazy writer ;) ) not because it was strictly necessary. You want to hate her, I think.
And the Horcruxes? They were told by Dumbledore to never tell anyone about them. D. reluctantly agreed that Harry told his friends, so he didn't have to do it alone. Dumbledore could have told Severus if Severus had needed to know. There was a reason why he wasn't told. I'm glad that I wrote the next chapter already. Do you think about the danger Severus is in now, knowing about all these Horcruxes – and Voldemort's reaction if he ever breaks through Sev's Occlumency?