1. Depends on how you connect it. I'd recommend using a mini-Toslink to use a digital optical connection between the Chromecast Audio and your receiver, then you will achieve the same quality as HDMI.
2. Stored on as in iTunes, no. You can however use your iPhone to play from Google Music, Spotify, Pandora, among others.
3. If you use the optical connection, it will use the higher quality DAC in your stereo.