They usually are but it's not a requirement.
Any celebration can be held at a synagogue, but any place can easily become a synagogue. In Greek, synagogue literally means "meeting house." Most Jewish celebrations tend to be held at a local synagogue, but celebrations can be held anywhere Jews can gather. During the Holocaust, Jews even had small celebrations in concentration camps.
Wrong. The seder is held at home, and the special festival prayer-services are held in the synagogue.
At a Jewish funeral home or synagogue or at the graveside.
Yes.
Yes.
At a Jewish funeral home or synagogue or at the graveside.
Unless there is some specific agreement between the synagogue and the relevant Christian congregation (such as a synagogue allowing Christians to pray in the synagogue on Sundays while the Christians' church is in repair), church services do not take place in synagogues. If by "church services", you actually meant "religious services," Jewish services in synagogues are held three times per day; in the morning, afternoon and evening.
In the Holy Ark in every synagogue (Jewish house of prayer).
Three.
If you have triplet boys, all three of them can be circumcised in the synagogue or at home.
Although the circumcision ceremony can be held in a synagogue, the normal location is in the home.
Prayer and Torah-readings. Other activities may sometimes be held: Torah-study, communal meetings, bar/bat mitzvas, etc.