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Welcome to the Motley Fool :)

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1. Can non-US citizens invest in the US stock market? (This is just to satisfy my idle curiousity.)

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You bet,

http://www.fool.com/FoolFAQ/FoolFAQ0041.htm

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2. Is it true that the same basic rules apply to all markets? That is, assuming I invest in the Australian
stock market, do markets behave in the same cyclic fashion regardless of where they live?

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All the major markets have their ups and downs. The main difference between U.S. and other markets is the much greater, and higher quality, flow of information one receives from public companies.

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3. Does anyone know of Australian Index funds they can point me at?

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I'm sure they exist. Try looking for leads on the Australia message board in the International Investing folder. Just hit Messages on the home page or Folders below :)

Patrick
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