The mikvah
Rabbis.
No.
They're called Rabbis.
What are the various types of Jews? Is there something called Asedic Jewish?
There are both Jewish Religious Day Schools and Jewish Sunday Religious Schools. These are not very different from their Christian or Islamic equivalents.
The person who leads the prayers is called a 'cantor'.
The Talmud.
The "cantor" is the person who does most of the singing in synagogue.
The Jewish religious teachers are Rabbis.
A practitioner of Judaism is called a Jew. A Jewish religious authority is called a rabbi.
Torah-scrolls. In Hebrew, it's "sifrei Torah."