Hi! I'm Bardic. And who would you be?

It's really sad that you feel ashamed of having autism, but I can't say I don't see why.
I don't think I ever had the chance to be ashamed, because I've known about my diagnosis for as long as I remember. Still, people do get genuinely surprised when I (as someone who's not a complete idiot) say that I have autism, and if I were someone else I could see how that would get taxing. And I do struggle a lot with feeling like I need to control myself and 'cover', even if I don't have an issue with the label its self.
Maybe we'll be able to help each other, even if it's just by assuring ourselves that we're not crazy.

See, I get what you're saying about it being unusual for someone to be completely average, but I don't think that could be called a kind of non-conformity since conforming is about being the same as all the other things. It would just be really, really weird and a bit boring.

What you have to remember about Hogwarts Houses is that they're something that was just made up by this person who is just an average person. Given that even the best psychologists can't come up with a four-group system to sort humanity (like, the Big Five is probably the best we have right now, and that's five sliding scales), it's impossible for her to come up with one.
In addition, the houses share a lot of traits (e.g., like you said, loyalty for both Slytherin and Hufflepuff; there non-conformity in both Ravenclaw and Gryffindor; learning in both Slytherin and Ravenclaw; and compassion in both Hufflepuff and Gryffindor; also, all the things in all the houses because humans do all those things), so there's going to be a lot of people who fit into all houses or two or three houses, and a lot of people who would start off with one house, but then change to another house after a huge event in their life (like a very average, nice person who's in Hufflepuff, then has a friend who gets screwed over by the law and goes full Gryffindor social-justice-warrior, which would be an amazing love story).
In short, don't take it too seriously since it's just a silly game we humans play like trying to decide which elemental dragon we would be.

So, if you want to learn more about logic I'd suggest just Googling logical fallacies and using whichever website is easiest for you to understand. I went to the extent of actually making a list of about 50(?) fallacies before I decided to stop, and even though I've never reviewed the list, writing them down made me really think about each one for an extended period of time and gave me an overall sense of how fallacious reasoning works.
Reading HPMOR is good not only for learning logic, but also learning how to do science, and it's just a really good story in general. It's kind of long, but if you have the time I'd say it's worth it. Though I should probably warn you that it might very well change the way you think permanently; personally, I think the change was for the better in my case, but it's always dangerous to do a ritual that requires a permanent sacrifice.
There's also a game called "Socrates Jones: Pro Philosopher". It's a simple flash game you can play for free online, and you basically have to find the flaws in the arguments of philosophers (it also has an adorable story). It's very good for learning more about fallacious reasoning and showing how it can be applied, and it doesn't take too long to play, either.
I suppose it's also worth looking at The Atheist Experience on YouTube or anything else that features Matt Dilahunty. He's very good at analysing the logic of something to an absurd degree--even to the point that you wonder why it matters--and then showing you why it matters. I've found his stuff particularly helpful in dealing with gaslighting and anti-LGBT arguments. I still have a lot to learn in applying it in the moment, but I'm managing a lot better than I used to before I found his stuff.
And finally, while it's not really a logic thing, it is an anti-gaslighting thing: Lily Orchard's Glass of Water series (well, some of it, at least) has also taught me a lot about applying reasoning. Specifically, she taught me that a stubborn adherence to abstract values is meaningless in certain contexts, and she taught me to consider the context before I apply a value. I don't know if you have to deal with any gaslighting, but if you're left wing and you're on the internet, you probably do. Like, you know how people will take the liberal value of freedom and use it to justify taking away the freedoms of LGBT people? How does that work?! Is that even allowed?! Well, after Lily's lessons of applying values in context, I find myself falling for that precisely 0% of the time when I used to fall for it (at least partially) 100% of the time.

Thanks for letting me blither on about Australia's geological history. I learned that fact about four years ago and this is the first time it's ever come in handy.