Seeking or Providing Explanations

I've read over Tae Kim's lesson relating to the の particle a few times to try to improve my understanding of it. It can be used at the end of a sentence to make it clear that we are providing or seeking an explanation for something, depending on whether the sentence is a question or statement. In my first example, I'm going to assume I'm talking to a cat-man, or a man who has the ability to transform into a cat, because why not. His name is Lee.

リーさん、猫？
リーさん、猫なの？

Lee, are you a cat?
Lee, you're a cat?

In the first sentence, I'm asking him a yes/no question. In the second sentence, I'm expressing surprise at the fact that he's a cat (because who wouldn't), and possibly asking him to explain WTF is going on.

With the second sentence I had to add な before の due to 猫 being a noun. I'd have to do the same with any na-adjective. I-adjectives don't require the な, though.

リーさん、忙しい？
リーさん、忙しいの？

Lee, are you busy?
Lee, you're busy?

Again, the first is a yes/no question, while the second is expressing surprise (and possibly dismay) at the fact that he's busy. The particle can also be used when you're providing an explanation for something.

Person A: 先生なの？
Person B: はい、先生なの。

Person A: You're a teacher?
Person B: Yes, I am indeed a teacher.

That's not the best translation, but the point is that Person B is basically saying "Yes, I am, in fact, a teacher" (while sounding more polite, in my opinion). If that sentence didn't have なの at the end, it would sound like "I'm a teacher" as a factual statement, and less explanatory.

Things get a little more complicated if I want to use the declarative だ or the polite です, because why wouldn't they?

Person A: 先生なのですか？
Person B: はい、先生なのです。

These sentences mean the same thing, just in polite form, but using なの in this case would be considered archaic or outdated. At first I was confused by this, but if you read it a few times, the なの does sound awkward when placed right in front of です. We can fix this problem by transforming the の into ん。

Person A: 先生なんですか？
Person B: はい、先生なんです。

I've bolded the ん to make it more obvious. Now when reading the sentences, I think they sound much more natural, and this is considered proper grammar. Not that the other isn't proper grammar, it's just outdated.

One thing that bothers me about this is that it sounds like the word なん (meaning "what") is being used here. So in reading or listening, it might be initially confusing because it's easy to read it as "what", rather than reading it as the appropriate explanatory particle. It takes practice, I guess. It's less of a problem with i-adjectives, where you don't have the な beforehand.

とても難しいんだよ。
It's really difficult, you know.

This may be a response to a question like "You're failing the class??!" where I'm explaining why I'm failing. I have the declarative だ used at the end, so because of that, my の becomes ん. It sounds much more natural in this case, as well.

I know there's more to learn about using の with other noun and adjective conjugations, but I'm going to pause here because this is enough for my brain for the day.

Credit goes to Tae Kim's lesson seen here.