They didn't. The Torah is the First Five Books of Moses.
Rabbis don't generally carry books with them because they are rabbis. If they do carry books, they can be any kind of books. But the name of the Jewish prayer book is the Siddur (סידור). Most traditional Jews carry a siddur with them, not just rabbis.
The Jewish Bible is not called the Torah. Jewish Bible, called the Tanakh, contains 24 books. The Torah represents only the first 5 books (Genesis through Deuteronomy).
See the attached Related Link for a synopsis of the books of the Jewish Bible.
5
There were small schools where the young boys learnt the Jewish books from Rabbis.
The Tanakh (Jewish Bible).
The Catholic Bible includes the Apocyra, which are Jewish religious books. These Jewish books are not recogonized as being authentic by most Jews, so they are left out of Jewish Holy books and Protestant (King James) Bibles.
I hazard a guess from your question that you are refering to the codification of the scripture in 80AD which limited those books in the "OT" defined as the WORD of God. The early Christian church used a greek translation of the OT, composed ca 320 BCE, as the basis of their "OT" which includes more "books" than recognized by the Jewish Rabbis. The Protestant Reformers based their OT on the Jewish "canon" of 80 AD ... thus the difference between the Catholic and Protestant Bible, and the difference in some of their doctrines.
A Yeshiva teacher is a professor in a Jewish religious college. The Yeshiva's purpose is to train rabbis and other religious related professions in the ethics, traditions, and precepts of the Bible (the Old Testament to Christians). In Hebrew, the word "yeshiva" means "academy". Therefore, linguistically speaking, one could be a Physics or Mechanics professor in a technical or vocational yeshiva. However, most (if not all) technical colleges in Israel that has "yeshiva" in its name incorporate Jewish religious instruction in the major part of their curriculum. Jewish instruction is concentrated on the Torah (the first five books of the Bible), the traditional scriptures like the Talmud and Mishnah as well as the rest of the prophetic and literary books of the Jewish Bible. A yeshiva has the utmost goal of training a wholesome Jew, whether to be a rabbi or a useful member of society.
See the attached Related Link for summaries of each of the books of the Hebrew Bible.
A Rabbi is a Jewish teacher, but rabbis in modern times also have other functions:Prayer leader (including weddings and funerals)Kosher food supervision (orthodox rabbis only)Religious counselingReligious school principals
It depends on the denomination, but the general answer is No. Even if it has only the books present in the Jewish Bible, as opposed to some deuterocanonical books, it have extra chapters in some of the later books (like Daniel) and the order in a Protestant Old Testament will certainly be different than the Jewish Bible.