Are you expecting Jewish-Americans throughout time to claim Israel as their place of ancestry
But I'm not expecting anything.

I just wanted to know what ancestries do they declare without having any
a priori expectations.
But - just as a side note - one of your points needs some clarification:
seven types of mitochondrial DNA, we don't know definitively, and who remained solely of one of those seven types?
Everyone has solely one type of mtDNA. Surprising? Not so much. Let me explain - mitochondrial DNA is inherited from the mother, and since you have only one mother, your mitochondrial DNA cannot get mixed or "multicultural" as you called that. Same refers to your Y-chromosome, the difference being that you inherit it from your father (and each person also has just one father, so you inherit "pure" Y-chromosome all the time - it cannot get mixed).
What you are looking for, on the other hand, is
autosomal DNA - all the remaining chromosomes, the rest of your genome.
This is what you inherit from all your ancestors in all lineages, so it can get mixed. But mtDNA and Y-DNA - no, they can't.
Take one of those genetic tests sometime for ancestry, and you might be quite amazed at how diverse your background is
Remember to order the test for autosomal DNA - if you order just mtDNA and Y-DNA (see above), then you won't find much diversity.
Anyway - I am still not convinced that the most interesting thing about ancestry is deoxyribonucleic acid.
Moreover - your DNA won't always tell you in which part of the world did your ancestors live, which ethnic group or nation they were part of.
For example if your ancestors were Jews from Germany, it is well possible that they had DNA typical for the Middle East or Southern / Eastern Europe, and not for Germany. So a DNA test will tell you that your ancestors lived in the Middle East or Southern / Eastern Europe, and not in Germany. Etc., etc.
DNA will also not always tell you about national identity of a person, his or her ethnic affiliation, religion, culture, and language he or she spoke.
A classic geneaology tree is better, but of course it has some limitations - because it only allows you to investigate recent generations.