>Is it possible to save a steaming audio (like Internet Radio) to an MP3 file?

Sure it's possible - you can save streaming *anything* from the internet to your machine, including videos. Obvisouly part of the trick is getting the HTTP or MMS or RTSP or whatever address of where this 'stream' is so you can capture it (they usually try to hide that from you)...anyway there are several ways you can get it - best thing I've seen thus far is HiDownload because it seems to have the ability to capture the most types...
Here take a look at this - it should point you in the right direction...hehe
http://all-streaming-media.com/record-video-stream/all-streaming-video-recording-software.htm