Direct sound recording software like
Audacity and
Replay Music records from your sound card. You can record anything with it, but you lose some quality when re-encoding audio.
Streaming audio/video rippers and
streaming audio rippers like
StreamRipper save the exact stream that is broadcasted onto your harddrive, so you don't lose any quality while using them.
So there are to types of programs that you can use, but sometimes it is really hard to find out from software description to which type it belongs.
I don't really know the proprietory format that
Audacity uses, but most probably it is lossless, so actually you lose some quality when converting these files to MP3s. Of course you can use some lossless audio codec like FLAC, but I don't really see any sense in that when recording 128 k radio stations.
To split MP3 files you can use freeware
MP3DirectCut. It does lossless splitting, so you won't lose any quality with it.