But if I do that, my music will not get copied into the iTunes once I play it, which is what I like it to do.
I guess I can't have it both ways, can I? Either it copies stuff or it doesn't. No way to teach it to handle different file extensions differently?
Yes, you can. Music is separate from books. Where do you buy your music from? I would imagine if from Apple it would automatically import it to iTunes. If from Amazon, there is setting in the Amazon downloader that lets you tell it what program to import it to (include iTunes).