You can call me a Hebrew if you want, but Jews and Hebrews are synonyms for us the Jews… or the Hebrews… or the sons of Israel.
The Palestinians do not pay the price of the Holocaust. It is a misconception promoted by some (I suspect knowingly).
Regarding the Ashkenazi, well, The Jews were dispersed and settled in different places. Some settled in the Northen Africa, some in Asia, some in Europe. I don’t think that settling in Europe makes you less Jewish in some way. I’m an Ashkenazi, and my ancestors lived for many generations in Europe. But if I ever decided to pass myself as a person of European decent, my Semitic nose would betray me every time. It is like the black Americans, who lived for many generations in the US. They could never pass as Anglo-Saxons and they did not become less black because of many generations living in North America.