I want to create a very simple liquid layout with 2 columns - the one to the left will have a fixed width, and the one to the right will be dependent to the window size.
1) If the container div is needed or not depends very much on your actual design, but from what I can see from what you have showed, it is not really necessary. What is body stuff?
2) You have answered your question yourself. If you want to prevent an overflow because of padding, margin,border, keep it.