The first two verses, yes, but you rarely hear more than the first verse sung, which is just as well since it gets increasingly irrelevant to modern Australian life as it goes on ("Brittania rule the waves!"). I didn't particularly try to learn it. I just have a good memory for song lyrics.
I know the national anthem of both countries, Sri Lanka my homeland and Australia where I call home now. As kids it was compulsory to memorize the anthem so I learnt the Sri Lankan anthem then. once I migrated I learnt the Australian anthem after singing it so many times st my kids schools.
No, I don't, and watchingit being sung at sports events etc., I don't think many other people know the oz. national anthem. Tony Abbott with his dames and knights would probably like us to be still singing God Save the Queen. I have heard some rousing anthems, but don't think ours is one of them.