All Lizzy's interest in Darcy's character really proves is ... interest. It doesn't mean that the interest in personal, or that she actually likes him. None of the other characters you suggest Lizzy should be interested in are particularly complex. Darcy is, and there aren't many complex characters in her life.

In addition to what you mention, Lizzy engages in repartee with Darcy -- but I don't think that is any indication that she likes him. Again, there are very few people in Lizzy's world that are up to that. And she talks to Darcy during the dance, the narrator says, because it would be a greater punishment to talk to him than not to talk to him. It doesn't sound like she talks to him because she likes him.

If Lizzy does like Darcy, why does the narrator tell us that "She liked him too little to care for his approbation" (also Chapter 10)?

I'm afraid you're going to have to be a little more specific. I can't see anything in Chapter 10 or 18, after re-reading them, that indicates that Lizzy thinks herself inferior to Darcy. Could you provide specific quotations?

What do you see of arrogance in Lizzy's treatment of Mr. Collins? She may think him a fool, and not without reason, but what do you see in the way she treats him that indicates arrogance? As far as I can see, her treatment of him is, for the most part, unexceptionable.

We don't really see much of Mrs. Hurst, I think think Lizzy treats Miss Bingley with a lot less disdain than Miss Bingley treats Lizzy. On balance, I'd say Lizzy behaves pretty well toward a woman who holds her in contempt and who treats her sister very badly.

I don't think the fact that Lizzy doesn't like having people look down on her makes her arrogant or vain. There may be a fine line between a healthy self-concept with a recognition of one's own value and arrogance, but I don't see any evidence that Lizzy crosses the line, at least not consistently.

What is wrong with Lizzy knowing she is smart and witty? After all, she is. She certainly does delight in the ridiculous, but that doesn't make her arrogant or vain, either. She doesn't use her intelligence or wit against people who can't defend themselves, as her father does, and in fact, she deplores such behavior. There are some things, like a man who has a resentful temper, that she considers shouldn't be made fun of.