Sorry I haven't responded to the questions--I've been away for a bit...
Yes, Nelson pretty much got it--I am (to my knowledge) 0% American Indian, and have never claimed to be. If you trace my ancestry back a few generations, and round to the nearest 1/8th, I'm roughly 3/8 Irish, 3/8 Dutch, 1/4 English, and 1/4 mix of darn near every other European country. However, I was born and raised in the United States, as were my parents. I'm not native to Ireland, or Holland, or England--in fact, I've never even visited any of those countries. I'm native to the United States--and thus, I'm truly a 100% Native American.
(Now, take my ancestry mix, and combine that with my 1/2 Italian, 1/2 Scandinavian wife, and our kids are truly a hodgepodge.
)
I believe TrainTrac is correct regarding the US government's terminology--they've been using "American Indian", not "Native American" on anything I've seen. Whenever I'm asked to fill out a form that asks my race (be it a government form, employer, health care provider, or whatever), if they use the term "Native American", I check it, as it clearly applies to me. If they use the term "American Indian", I don't.
Caymen's point about the use of "Indian" in "American Indian" is quite valid. Which is part of the reason why, when referring to an individual, I far prefer to refer to their specific tribe ancestry--Sioux, Apache, Chippewa, etc. However, that obviously doesn't work when referring to those tribes cumulatively. In that case, I haven't heard of a more appropriate term being developed yet. I've heard "Tribal American" a time or two, and I think it's a decent possibility--but it's clearly not all that well adopted as of yet.