Only the Pharisees survived and became today's Jews.
The Sadducees were Jewish. They did not believe in the authority of the Oral Torah. Eventually they degenerated into a group of thugs who attacked the Pharisees whenever possible. The Pharisees, needless to say, didn't like that much.
Typically, they are called Diaspora Jews or Jews of the Diaspora.
They were (and are) known as "Diaspora Jews."
Diaspora
The return of the Jews from the Diaspora.
If you are referring to the Jewish Diaspora, then it was the Jews that experienced it.
The scattering of Jews outside of Judah was called the diaspora. Please see related links.
No.
The diaspora, or the exile (galut). See also:More on this topic
Exiles; Diaspora JewsSee also:More about the diaspora
The Exile of Jews from palestine is known as the Diaspora
Diaspora communities; exiles; yordim (in recent usage). See also:More about the diaspora