I think it's probably safest to have all the application stuff in by the 30th of November, but I would recommend calling up the College of Arts and Social Sciences to double-check. Their number is 02 6125 2898.
Is the sample a personal statement as to why you want to do the course? If so, I recommend writing things like: you enjoy a challenge, you are interested in pursuing a higher level degree like a PhD and being a researcher, and that you can demonstrate that you could fulfill the requirements (put in examples of what you've done to show this). Basically, ANU wants graduates who will make ANU look good, so show them that.
With the majors, it kind of depends on what your major is in, but emphasise how your work will help the world/other people as well as your passion for that area. ANU seems to like that kind of stuff.