No. The radio plays your own songs from the Music Folder you pick in the add-on preferences. The rain sound is built in.

It only draws on top of the interface and writes nothing into your .blend. Rain and stars pause during renders and animation playback. If a heavy scene feels sluggish while it rains, lower Animation FPS or the rain Amount.

Yes. Only the rain and stars pause during renders and playback; the radio keeps playing.