as Synagogue is to Jew
Maybe, if it's a non-denominational synagogue.
No. Jewish custom is never to enter the house of worship for another religion.
It depends on how pious they are. A religious Jew will pray three times a day at the synagogue (although two of the prayer services will be done together). Secular Jews can sometimes go years between entering a synagogue.
No, but they are banned from being full-fledged members of the Jewish community.
A synagogue is a Jewish house of worship, study, and assembly, but anyone can enter.
Prayer, Torah study, discussing communal affairs, and weddings.
A synagogue is the place where a Jew preys to God. A synagogue is a temple, just like a mosque or a church. A synagogue is led by a rabbi (Jewish priest) and the service often involves preyers in Hebrew.
No. A Jew is Jewish even if he hasn't been circumcised. However, this Jew would be unable to eat from the Passover sacrifice.
it depends on the rules of the synagogue, religously in is not prohibited
In the Bible, the term "uncircumcised" is often used to refer to those who are not part of the covenant with God, as circumcision was a sign of that covenant for the Jewish people. It can also be used metaphorically to describe those who are spiritually hard-hearted or rebellious.
Yes, non-Jews attend Orthodox synagogue services all the time, usually as an invited guest to an event. If you wish to attend a religious service at an Orthodox synagogue, you might want to contact the synagogue's rabbi first to determine the best time to attend. As for being circumcised or not, it doesn't make a difference as male circumcision is only a concern for Jewish males. As non-Jewish person can't participate in a Jewish religious service anyway, being uncircumcised is a moot point.