From the main player window, swipe left anywhere on the screen to access the music index screen.
No.
iOS Settings > CarAudioDeck > Deck
iOS Settings > CarAudioDeck > General Settings
Connect your iPhone to your car stereo via an AUX cable, play your music through Apple Air Play or connect your device via USB to Made For iPod stereos.
Yes, simply hit shuffle icon at the top of a playlist or list of songs.