Origins of people in the USA

It common usage, though, Jews are seen as an ethnic group. You almost never hear anyone say, "There are 2 million Hebrews in New York City." 

Sorry, I don't think I understood everything properly, but from what I got out of it:

There are about 6 million Jews in the United States. (more than in the country of Israel) Most are descendents from the European Jews, rather than the Spanish/Middle Eastern ones.

I think the difference between Hebrews and other Middle Eastern people, besides not being an Arab language (though an Afro-Asiatic one), is that they have brought with them a significant non-Palestinian bloodline.

I've heard about the Khazars before. Interesting stuff. However, I think most modern Jews are descended from Jews who settled on the Rhine river and were forced further East as centuries passed. Obviously there was some conversion among the Turkic tribe, but I've read it was only the aristocracy who really converted. Those Jewish peoples probably migrated West and merged with the others in Poland. (Not that I've read that before...just something that seems to make sense to me)

Or, they could have gone further East and become the Central Asian Jews, too. You never know.

For the Scottish and Irish influence, look at military funerals, sometimes "Amazing Grace" is played on the bagpipes. We obviously have way more of a British influence, we speak the language, and we have taken some words from specific dialects (like in Western Pennsylvania, both "Yinz" and "Nebby" come from Scotland).