First you need to make sure you are eligible to apply for US citizenship.Minimum age of 18 years during which as a green card holder you should have stayed for 5 years at least with continuous physical presence in US.
Next you need to use the Form N-400 to apply for US citizenship. Which on approval and subsequent to the citizenship test you would become US citizen and get a naturalization certificate as proof.
yes through paper work and then you are welcome to come to the us as a us citizen.
A naturalized citizen.
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 of course. You are a US citizen, you said so yourself.
No, its no mandatory. but its just that if your a citizen, you can vote, easier to travel outside the US, and sponsor relatives to come to USA.
yes if you stay they will send you back
Marry.
If they obtain a visa, they are not illegal.
Can an illegal alien who was deported and barred for ten years come back sooner by marrying an us citizen?
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.
Marry In Aus.
contact I N S - they can give you info