Well... Yes and No...
YES: You CAN play movies in things like iTunes and move its window to the TV display (in Extended Desktop mode) and at the same time, work on other things on the main computer display.
NO: You can NOT play a movie in FULL SCREEN MODE on the external display (tv) and still work on your main computer display. When you enter into Full Screen, the other displays go completely black and if you click out of that mode (like back into Finder), then you lose out and pop back out of the Full sized video.
It IS POSSIBLE to just manually drag the movie window to its maximum viewing size (almost full screen) and still be able to work away with other apps on your main display. The Downfall of doing this is that on the tv, your movie will be partially showing the Top / Bottom window frames. But that's it's... the video is still ALMOST the whole entire TV screen.
Having independent audio (movie playing application plays its audio through hdmi, browser through the regular mac audio ) would be ideal
but not strictly required.
Nope... this one's is a bit tougher (as in not do-able). In the System Sound Settings, that is where you set your Audio (which is EVERYTHING that your Mac is playing.. beeping... chirping...) to either play thru your internal speakers or to be sent OUT via HDMI to those speakers on the tv, etc. It is unable to split out audio to different sources from different applications.
Hope this helps...
it'd be nice if on a two screen setup one app could go full screen without impacting the other screen
and for the audio - I thought that was far-fetched.
VLC allows for audio device selection, don't know if it can bypass the system prefernces
but in any case it may not be able to play videos rented from itunes with DRM