Is it possible to turn off the screen while you are "listening" to video songs . I mean I have downloaded some 100 video songs and I sometimes I would just listen them for example while driving, and to conserve battery i would like to shut the screen off just like it does while listening to audio.

If you press (tap) the power button on the top of the phone, left side, it will cycle the screen brightness. If you hold this button down, it will turn the phone off.

Edit: Just tried this with a video I still had on my phone. Once the screen is off, the video automatically pauses. Too smart for it's own good.