iTunes Radio produces a quite messy and incomplete list of stations. How can I tidy it up and add my own favorite stations ?

There's no way to add a station to the Radio section of iTunes, since that list is provided by a server somewhere. There are two different ways, though, to add streaming stations to iTunes depending on whether you know the direct URL to the stream or are adding a link from a broadcaster.

If you have the direct URL (and it needs to be the URL directly to the stream, not a link to a web page), in iTunes go to 'Advanced' and then 'Open Stream'. Enter or paste the url and the station will begin playing. The link stream then be in your library and you can, if you wish, drag it to a playlist.

To add a playlist from a broadcaster such as Live365, go to the broadcaster and select the station you want. The playlist (a .pls file) should download to your system. If the station does not begin to play in iTunes automatically, double-click or drag and drop the .pls file into the iTunes library window and the playlist's stream will be added to your Library. Again, once in the library you can drag it to your own playlist if you wish.

As to when, or indeed if, Apple will make any changes to the Radio section, no one here can say.

Regards.

Find a particular radio station in iTunes? contains information relative to searching through iTunes' radio stations.