How to download an audio file from a web site on iOS? Is there a way to download an audio file, such as a mp3-file or a Quicktime-file from the iOS Safari browser to the device so I could listen to it later when I'm offline? Is there a way I should program the web site to make this possible?

I'm not looking for an additional app to help me achieve this.
No.  This is not possible at this time without using a third party app. I use GoodReader for this—and other—tasks.