Yes you can listen to STAR1079.com on a smart phone. I use http://www.yourmuze.fm
to play the station through my Droid. They do have a new app, but I haven't tried that yet. I just added STAR 107.9 to 'My Stations' at Your Muse and selected the bit rate I wanted to receive it at and I can enjoy the music. The nice thing about Your Muse is that you can adjust the bit rate, so if your phone can't handle 128Kbps, you can down size it.
As for the "Mix Talk", you are correct. We switch our stream to that on Wednesday and Friday mornings at midnight for about 55 minutes. Kind of a barter deal I'm doing with Mix Talk.