(a) No, that's wrong. There are many different models of democracy in the world but Australian governments are an example of the type that is generally described as 'representative democracy'.
This means that governments are elected periodically by winning the support of a majority of voters at an election. But in between elections, the elected government 'represents' the voters, making decisions and implementing policy on their behalf.
Importantly, in between elections, the government of the day has control of the processes for making, administering and enforcing the law.