Often it is placed in the front, near the lectern at which the person stands who leads the prayers.
In many cases yes, but not necessarily.
I'll assume you're referring to Hanukah. the menorah (candelabrum) is lit by each Jew in their home; but Hanukah is marked in the synagogue as well, with Torah-reading each day for the eight days, and a couple of additions to the daily prayers. It is customary to light a menorah in the synagogue too.
These are common: a menorah (7 branch candelabra), and/or a representation of the Asseret HaDibrot (Ten Commandments) in a synagogue.
A menorah has 7 branches, to represent the 7 days of Creation. (There is also a specialized menorah for Hanukkah, called a Hanukkiyah, which has 9 branches, but there is nothing with 6 or 8 branches.)
In a synagogue
A synagogue is the equivalent of a church but it is Jewish. Inside there is the ark which holds the Torah, that's like the bible, and the menorah that covers the Torah. There is a women's and a men's section.
You would find it either at the front or centre of the sanctuary.
Hanukkah is a minor festival, during which the menorah (Hanukiah; candelabra) is lit at home. In the synagogue services, certain prayers and Torah-readings are added to the usual weekday services.
The ark is known as the Aron Kodesh (ארון קודש) and it contains the synagogue's Torah scrolls.
In the home and in the prayer-services. See also:http://judaism.answers.com/jewish-holidays/hanukkah
We don't know where the ark is and it has never been in a synagogue. It had been in the temple in a room called the Holy of Holies.
My best recommendation would be in a church or synagogue.
In a synagogue