Canada

"Aborigine" is not "comes from away". I don't know where you're getting your etymology from, but it comes from the Latin "ab origine" which means "from the source" or, in context, you know, THE ORIGINALS. (First used, incidentally, to refer to the people living in what is now Italy before the Romans took it all over.)

Aboriginal is "ab origio", literally "from/since the origin/beginning". Already the Romans used it in the sense of "there from the very beginning".

Indigenious is "indu gignere", "begot within". The "place" part is implicit. More of a "native" thing as in "natively born American" but the meaning shifted from the original Latin.

Practically, nowadays, they're synonymous. Over here we use "autochthon", literally "self earth/soil". Also used in geology and biology. The constitution speaks about "national minorities and ethnic groups", going by the last recent arrivals 600 years of living here as an ethnic group suffices for autochthone minority status. Though in our case there's no settler-colonials which of course changes the equation.

Uh, no, many of us prefer to be called by the nation we belong to. Some of the younger ones would be really offended at being called Indian, especially by white people. Indigenous, First Nations, and native are fine - better than Indian at least.