Can VLC media player stream iTunes library to TV?

For VLC questions you are better off asking on VLC's support site. VLC doesn't use iTunes' library structure. It simply plays media files from its own playlist which is primitive.

Why bother with this "streaming" thing? We plugged a MacBook Pro retina into the HDMI slot of our Samsung television last week and after tweaking a few settings it was mirroring audio and visual to the TV set. You play a movie with VLC and it appears on the TV.

VLC can't play the DRM protected content (namely all movies, and some pre-2009 music purchases) from the iTunes Store. If you have other movies or music it can play the content that is in iTunes by playing the same media files, but the content structure you see in iTunes isn't something shown by VLC. As for full streaming directions you really need to ask on the VLC web site since that has nothing at all to do with iTunes.