A Zionist is any person, of any religious background, who supports the concept of a Jewish nation existing.
No. There are so-called Anti-Zionist Jews who also support the concept of a Jewish nation existing.
However, they say that under current circumstances it is bad for Jews to live in the Land of Israel.
(Most of them say so because they live in the rich and secure Western countries and don't want to leave)
Zionism is about Jewish right and obligation to live in Israel.