Assuming the questioner is asking where the 10 Statements are located in a synagogue, the answer is that if a synagogue has the 10 Statements on display, they are usually located on or above the ark containing the Torahs at the front of the prayer sanctuary.
They can be displayed anywhere in the synagogue (often they're over the Holy Ark, or embroidered on its curtain).
These are common: a menorah (7 branch candelabra), and/or a representation of the Asseret HaDibrot (Ten Commandments) in a synagogue.
A good place to begin a search for an answer is Exodus chapter 20, especially the beginning of the chapter, where the first of the Ten Commandments is stated.
Commandments.
The Torah is read in synagogue more than two hundred times each year, not just on Passover.
There are numerous synagogues in Mea Shearim. There is no "main one" -- as each community goes to its own synagogue.
Each synagogue has its own Rabbi. Some communities have a Rabbi whose authority is more widely recognized, but not all.
The institution of the synagogue appears to have originated between the time of the Babylonian exile an the time of Jesus. There were no synagogues before the exile, and there were lots of them by the time of Jesus. Nobody knows who built the first one, nor do we know whether it was built in Babylon before the return from exile or in Judea and Galilee after the return. It is almost certain that the first synagogue was organized using an existing building, and that the institution of the synagogue was around for a while before the first purpose-built synagogue was built.
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.
Exodus, the giving away of the Ten commandments, construction of the Temple at Jerusalem and the worship in Synagogue after the return of the Jews from Babylon etc.,
There is no Hierarchy The Rabbi is the head of each synagogue then there is a cantor and the people.
Portions of it are read, several times each week.