<< If you have a single video card with TV out, does that mean you can have your monitor connected via the VGA interface and the lcd connected via TV out at the same time? >>
Depends on the video card.
I had an old Jaton AGP that couldn't, you had to choose one at a time. However, I had an old S3 AGP that could. The S3 could only display to both TV & monitor simultaneously if the resolution were 800x600 or less. It was also the same image on both displays.
I don't know the capabilities of most of the newer video cards as I haven't bothered playing around with the TV out on any of my newer video cards since the TV is no longer in the same room as the computer.