Great questions and if I may... Welcome to Trek Radio! So happy you found us.
Trek Radio is an internet radio station, but that does not mean it is confined to a bulky PC. There are several ways to listen to Trek Radio on the go, including an upcoming Trek Radio App! But, if you cannot wait a few more weeks for that to roll out (and honestly, who could blame you with all this awesome) there is a great solution that I have recommended before, and in fact use myself:
http://tunein.com/mobile/It is a paid app on iPhone, but free on platforms such as Android. Start it up and do a search for Trek Radio and add it to your favorites. It's as simple as that.
Now, as far as Star Trek music on a Star Trek radio station... We have several DJ's who play a lot of Trek music, most notably DJ Cohas. But you can bet every DJ here has some Trek in their libraries. Which brings me to a great new addition we are rolling out: DJ specific request lines!
http://www.trekradio.net/community/requestsGo ahead and check out our libraries. Requesting that fabulous Suite from Inner Light is only a click away! And if that doesn't do it for ya, every DJ monitors our IRC chatroom during their broadcasts.
http://www.trekradio.net/community/irc-chatroomLog in there and tell us what you want to hear! We are above all else,
your radio station.