NO ... but PS2 games work on PS3 consoles ...
Yes they do. It works the same with PlayStation games on PlayStation 2 consoles.
Games work on the console they were designed for and are not interchangeable.
no
No. US games are NTSC while Australian consoles only play PAL games. I think that Australian consoles should work with European, Indian, Chinese and Brazilian games but not American, Canadian or Japanese.
it depends on the console
no they do not and can not be made to work through software changes updates or added hardware
yes
Yes, DS games and consoles are not region locked.
the ps3 is region free for ps3 games, not for ps1 and ps2 games tho
Yes, Australian games will work on a UK PS3. In fact since the PS3 has no region lock whatsoever, you could even play American and Japanese games on it.
No Nintendo DS games work on Nintendo DS game consoles and maybe some other Nintendo and not on any of the Xbox or PlayStation game consoles regardless of the country or region.