Although I do feel flattered, but my Severus isn't canon Severus. He's like I saw him (and still see him to some extent) after book 6 - and I don't see him as all that much damaged. He is tough and gets over these things, although he does have a vengeful streak and never forgives some people. However, he never hated Hermione, nor wished her ill. And that is even confirmed in book 7: don't call her a Mudblood. Why would he care if he hated Hermione?
But anyway, in the story, he's been confronted by her, in a most emotional way, as his Price persona. She told him about her trust and pain to have been so deceived. And later, in the Occlumency lessons, he feels her trust. How can he not, teaching her. And it's a sign of his trust that he doesn't try to find out all her 'misdeeds'.
That 'past sins' comment? It was teasing. They both know what a handful the trio was, after all. And he certainly wouldn't want to know how many times they broke the school rules. And she knows that, too. These are things from her childhood, from the past. They both can smirk about that.
We have to agree to disagree. I think Hermione is very smart - but not very wise. And being used to having to do so much on her own, she has a hard time taking that guidance when it is offered. Which is complicated by the fact that she now is in love and really doesn't want to see Sev as a guide and a teacher. Which makes people prickly.
The Art of War may read as a work of great wisdom - which it is in a way - but it is also very cruel. Did you ever look at the commented version? Severus' teaching from that book doesn't mean teaching morals and compassion. It means teaching tactics and winning.