As an Italian in Australia for a while, I noticed this very common use of "how are you" as a greeting to welcome you into a shop, and customers answer with a second "how are you". A stranger, in Italy, will never ask you such a question, you don't know him, he doesn't know you, and "common sense" imposes a "good morning" or similar, not even "hello", too friendly.
This is why is NEVER got used to that, and every time I ended up stuttering something like "fine, how are you", or just "fine" inevitably feeling a bit stupid and/or awkward. Point is that I couldn't help myself putting the actual answer ("fine") in my formal answer ("how are you?/and you?").
My questions are
Don't you feel the weirdness of answering a question with the same question? I understand that's common use, but to me that's something really confusing, I had a hard time trying to deal with it.
Every time I answered with just "fine, I was looking for a book blablabla..." I thought "ok, that was wrong, I said 'fine' and nobody does that, I didn't ask 'how are you' and everybody does that." Was my answer actually impolite (or something else) because of these two reasons?