They remain where they are
to try to find family.
To return to their ancient land.
Zionists
DP stands for Displaced Person. This is a reference to the Jewish persons that were forced into death camps by the Nazis and then liberated by the Allies in WWII. These people were still unable to return home to Germany or stay in countries like Poland because of the remaining climate of Antisemitism This ultimately led to the formation of the Jewish state, Israel.
They were readmitted to England by Oliver Cromwell in 1657.
Albert Einstein was not "thrown out of Germany." He left Germany to visit the United States in 1933 and when Hitler came to power he chose not to return because of the anti-Jewish conditions that Hitler's rise to power portended.
The key decision was taken by the United Nation.
Israel's law of return guarantees citizenship to all Jews. (There are issues and debates about the definition of who is a Jew, and how you prove you are Jewish.)
He returned to Germany in 1931.
Hessia is a province of what we now call Germany. If the Hessian soldiers did not return to Hessia then they may have returned to Germany
All nations of people have unique experiences and so all peoples are in some ways unique. The exile to Babylon certainly did not make the Jewish people especially unique, but the permission to return was probably unique in history. Only some of their contemporaries, also exiled by the Babylonians, were ever afforded this chance. So the Return from the Babylonian Exile was the one great event in Jewish history that made them truly unique.
zionism - "the national movement for the return of the Jewish people to their homeland and the resumption of Jewish sovereignty in the Land of Israel, advocated, from its inception, tangible as well as spiritual aims."