Do Polish native speakers use that, or do they tend to use pisarzem even when talking to a female?
Actually modern Polish language slowly goes towards trying to create new feminine forms where there used to be only a masculine one, so such a basic word as "pisarka" is definitely a necessity ;)
Is it only someone who writes certain things, or can be writing both stories and songs i.e?
Nowadays „pisarz” means only „author of books” (usually romans). In the old days when the literacy was much lower it was an occupation. Also some officials were entitled „pisarz” like „pisarz wielki koronny” (łac. notarius magnus). In modern Poland this kind of job is known as „notariusz” (notary)
I'd say that it's someone who writes books. Stories may undergo this definition, but not necessarily songs.
No. Unless they write a book, perhaps. But still, there is a separate word for a journalist: dziennikarz/dziennikarka, so even then he/she would probably be rather treated as a journalist who wrote a book.