I don't really get why the cut video won't play after the cut. To be honest, it could very well be that Nuendo didn't solve that problem for me either, I just accepted it and worked around it. I simply use multiple projects for these purposes now.
As far as the "Import audio from video file" goes, that has alot to do with the video file and codec. I know for instance that sertain quicktime files have a kind of build in rip-protection, which you don't notice when simply viewing the file, but which doesn't let you extract the audio from the video file in any sequencer program. Also, the audio might be encoded in a way that Cubase/Nuendo doesn't recognize is, like Real Audio/Video. If you really have to get a hold of the audio from a video file, and there's not other way you can obtain it, then use the output to input method, either by routing a short cable from the outputs of your soundcard to the inputs, or use software to do it (can't help you with that).
I often find that when working together with video people (editors, 3D animators etc.) they know less than nothing about audio, delivering mp3 files to you, simply boosting the signal way over the red line simply because "it wasn't loud enough", delivering you video files in some supernew codec that requiers a more than super computer and video card with crappy audio encoded somewhere deep into the file (if you're really unlucky, mono and at a horrible bitrate aswell). Inform them very, VERY well before hand how you want things and refuse to do any work if they don't deliver it like you asked. Perhaps that's not the case with you, but I just wanted to rant about that a little bit
