Yes, banks in Australia are required to be licenced through the government.
The biggest banks are commonly known as the big 4, these are Commonwealth Bank of Australia (CBA), Westpac, ANZ (Australia and New Zealand banking group) and NAB (National Australia Bank).
APRA (Australian Prudential Regulation Authority) regulates banks in Australia.
Most banks offer some form of high interest savings account. Sometimes these are online only offerings and may have restrictions attached to be able to get the higher rate of interest.
HISA stands for High Interest Savings Account. This is a product offering a higher rate of interest on your deposits.