What is Australai's place in the world? Also, what is Australia's role in the UN?

What do you mean by Australia's place in the world?

This site explains Australia's role in the U.N.

http://www.dfat.gov.au/un/

You also may want to check this site.

https://www.cia.gov/library/publications/the-world-factbook/geos/as.html