- The Govenor General is appointed by the Monarch as their representative. The government recommends a candidate. There is nothing (as far as I'm aware) to force the monarch to appoint the individual versus anyone they want. This would be a constitutional crisis.
- The Govenor General has kinds the same powers as the monarch. Legislation requires "royal ascent l" to become law (similar concept to the US president signing bills passed by congress). The Govenor could reject the bill, but that'd trigger a constitutional crisis.
- The Govenor General holds similar powers to the executive of the US (using them as an example because if you are on an England speaking site you probably have some familiarity of the US system via media). But based on recommendations from the Prime Minister defers these powers to different ministers. Commonly referred to as a Portfolio. Eg how we a minister for defence, immigration etc etc. Failure to follow government recommendations would trigger a constitutional crisis.
- The Govenor general can sack government and trigger an election. The closest Australia has been to constitutional crisis was the time this power was exercised with the sacking of Gough Whitlam.
(note this is all based on my memory and understanding from classes in high school long ago)