Starling is a graphics API primarily. As such it does not have any support for audio, but it is easy to hook audio into it. Or run the audio from your own code, with the same events and actions driving the audio and the graphics.
No, Starling is not becoming obsolete. Flash Plugin is being retired at the end of this year, but browser gaming in Flash is only a tiny fraction what it once was. AIR/AS3 are used mostly now to make apps for iOS, Android, Windows and Mac.
Starling is well suited for these, letting you leverage graphics acceleration on all of these platforms. On mobile in particular the classic Flash drawing API is no longer supported, you have to use Stage3D, and Starling provides a higher level API which takes care of most of the details of that.