Is the CarPlay API
publicly available?
Where can we find a programming guide or the reference to these classes if it is?
Or will it integrate seamlessly with other APIs like Audio from AVFoundation
?
The MusicCarDisplayUI.framework
framework is a private framework as of iOS 7.1. Taking a look at the runtime headers of the framework, one can guess why; it's just not ready yet for wide use. Whether Apple will make it public in the future is one's guess.
In the meantime, make sure to open a feature request or directly contact Apple here.
Update: If you wish to have a CarPlay-enabled app, contact Apple using this form.