It is hard for you to just stay in Australia and not working. Unless you keep studying, you can stay for a period of time. After you finish Uni, you may apply for PR.
You can buy porperty in Australia, but you need to buy new porperty, not old or second hand porperty. Anyone can buy porperty for investment. After you buy the porperty you may apply for PR as well. I think you need AUD$ 500,000 for migrant to Australia.
if u want to live permanenty in aussie.
u hv to get a PR. permanent residency.
but u dun need a citizenship if u dun want.
but itz a kind of immgration . u can go thru different channel to get this.
depends on how kind of citizenship u r holding, wat kind of visa u wanna get to stay in oz. ur personal bg, etc.