Dear Max
Thank you for your questions and for following me.
It's difficult to answer your question because there is no definite and accepted Jewish position on these matters. On the other hand, as a Reform Rabbi, I confront myself every day with the tension between particularism and universalism, both inherent to the Jewish religion.
Reform Judaism was born at the time of the Jewish Emancipation, out of the attempt by German Rabbis to transform Judaism into a universalistic faith and German Jews into German citizens of the Jewish faith - and it failed. Germany was the place where antisemitism raised its head and shattered all the illusion of acceptance and assimilation of the Reform Judaism project (which later blossomed in America with a more particularistic/ethnic connotation).
So, trying to answer your question. Jews are a community based on the observance of mitzvot and on a common shared memory. Some of the mitzvot are universalistic -the famous Love your neighbour as yourself- some are not (for example, all the agricultural law regarding the land of Israel). It would be intellectually dishonest to erase one kind for another.
The Jewish shared historical memory is another minefield for universalism, as it implies mourning the Destruction of the Temple in Jerusalem (before the Holocaust, the most tragic event in Jewish history), which is a very particularistic event.
To answer your other question.
Those Jews who, like me, do not believe in a personal Messiah believe in a Messianic kingdom, a future of peace for all humanity when no life will be desecrated by suffering and needs. We are actively engaged in the holy work of bringing this Messianic kingdom on the earth. It's a concept called "Tikkun Olam", rooted in Jewish mysticism. Because of its mystical root, we lack details. There is no excellent agreement on what this Messianic kingdom will look like and what we must do to hasten its coming.