Meaning of かな for asking questions

Question

I'm reading Yotsubato to learn Japanese. On page 98 of Tome 1, Asagi asks Yotsuba:

クーラーって　知ってるかなー？

I understand she's asking if Yotsuba knows what an air conditioner is, but I'm unsure about the nuance brought by the use of か and なー here.

From Tae Kim's guide,

The question marker 「か」 is usually not used with casual speech to make actual questions. It is often used to consider whether something is true or not. Depending on the context and intonation, it can also be used to make rhetorical questions or to express sarcasm. It can sound quite rough so you might want to be careful about using 「か」 for questions in the plain casual form.

So which is it here? It doesn't seem like she's trying to sound rough or sarcastic.

Also, is なー　here just a way of saying な, itself just a way of saying ね (I'm still quite confused with all the sentence-ending particles)? What would be overall an accurate translation of the question?

Answer 1

From WWWJDIC:

かな ； かなあ

1. [prt] ▶ (at sentence end) I wonder
2. [prt] ▶ (at sentence end) should I? ▶ is it?
3. [prt] ▶ (at sentence end) I wish that (with a negative) ▶ I hope that

In this context, かな functions as "I wonder...?"

知ってるかなー？ would translate as "I wonder if you know (about)?" It's a more indirect way to ask than 知ってるか？

As you mentioned, か is used to designate a question. な (or なあ, なー, etc) can be used at the end of sentences to colloquially indicate wondering.

そう思っていたなー？ - That's what you thought, huh?

As opposed to

そう思っていた. - That's what you thought.

Definition Source: WWWJDIC at http://wwwjdic.com