You do not have to be a "US Citizen" to live in the United States but you do have to have some form of legal status to be legally resident. Those alternative forms of legal status may include:
Yes they can live together
Australian female citizen marrying US male citizen - which would be easiest marrying in US and come back to Australia to live or marry in Australia to live?
Yes, but the US citizen should sponsor his/her spouse's immigration in order for him/her to get a green card.
Permanent resident can apply for US citizen after live in US for 5 years (continuously and not leave the US in the period of 5 years).
You can but be aware, that the UK citizen cannot legally change their status while in the US. It depends on where you both want to live. If the US citizen wants to come back to the UK, a marriage visa is needed from the British Embassy in the US. However if the UK citizen wants to live in the US, they will have to go back to the UK and the US citizen will then need to file the I-130. Until it comes through you cannot live in the US, but will have to wait in the UK.
NOPE
You must live in France for several year while applying to be a French citizen.
Marry In Aus.
yes because its a us territory.
If you are legally in the US, you file in the state where you live. You do the same thing as a citizen of the US would do.
Puerto Rico is a US Territory and its inhabitants are US Citizens! So, if they are US Citizens, any US citizen can live in Puerto Rico.
no you must be U.S citizen vote