What screen does the idrive deafult to when the car is powered on and not in use? Can you select your own screen and does it stay on the whole time the car is on (driving) or does it go off like a screen saver?

The main menu screen with the five initial options.

I don't think you can choose another.

I haven't been able to.

Does it display a clock and/or radio station?

There is a small strip on the bottom of the screen that displays time, climate settings, radio station or CD even if you don't choose an option form the main screen.

main screen, any selection, or display off...
display off leaves the info strip on: climate, time, RDS-radio station/CD#&track