The term "Native American" has two meanings.
Sure. Native is an adjective implying a sense of permanency or belonging. I have heard the phrase "Native New Yorker" to mean someone who spent all their lives in New York city... as opposed to the tourists or transplants.
The Nativists, as in people who are opposed to "foreign" influence in the United States, are almost always descended from northern Europeans.
I will let Woiyo answer for himself as to whether he has ancestors who were in North America 1000 years ago. I suspect not.