If you are specifically talking about Jewish beliefs and the Jewish religion, then no, they wouldn't have spread as widely. Judaism as a religion spread to multiple countries because Jews as people spread to multiple countries. There was no mass conversion of indigenous populations when they moved from place to place. If Judah and Israel had never been conquered, Judaism likely would have remained solely in what is now Israel.
If you are referring to Jewish values, many of these were taken up by Christianity, such as the Jewish value for all human life (in contrast to the Greek value of useful human life), monotheism, the concept of a day of rest or week-end, and the idea of enumerated ethical laws. These values spread to Europe on account of Christianity and would have spread widely due to the European conquest of the known world.
Perhaps yes, since it was the daughter-religions (Christianity and Islam) who did most of the spreading of these beliefs and values. See also: The influence of Judaism
In contrast to some neighboring countries, Israel has no state religion, though most people in Israel are Jewish.
It was set up for the Jewish peoples to have a homeland.
See the attached Related Link.
Israel is a Jewish country. They believe that Jesus was a prophet, but not the son of God.
The Hasmonean Kingdom, which was the last Jewish State in the Land of Israel prior to the Modern State of Israel, was defeated and conquered by the Romans in 37 BCE.
Assyria and (later) Babylonia.
There is no such thing as a Jewish Church. Judaism doesn't have that kind of organization. Jewish beliefs originated in the land of Israel and evolved all over the world.
look here http://www.jewishvirtuallibrary.org/jsource/History/exile2.html you will see the whole timeline
Israel´s history began about 3,000 years ago in the Land of Canaan, which was later called "Eretz Israel" - The Land of Israel- and then, after the Jewish revolt by Bar Kohba,was renamed in "Palestine" by Romans who conquered this land
75% of the population of Israel is Jewish.
Israel is a Jewish state, but 20% of its citizens are not Jewish.