After the prophets, it was the sages of the Talmud (and then later Rabbis) who handed down the proper understanding and commentaries of the Torah, Nevi'im and Ketuvim.
Moses
It's a lifelong study.
By thinking deeply into the prayers and during Torah-study.
Torah-study is an intrinsic part of Judaism. Many synagogues have Torah-study classes before or after the prayer services.
The Torah and Talmud.
The central moral message of the Torah is this: What is hateful to you, do not do to another. The rest of the Torah are details. Go study.
According to Jewish tradition, we should study the Torah whenever possible. The Torah is vastly important, and wide in scope; and life is short. We believe that the Torah instructs us, improves us, and sanctifies us. Those who do not take it upon themselves to study Torah full-time, should set aside some time every day for learning Torah.
Of course they can
Absolutely. One may and should study Torah on Yom Kippur. The only day that there are some restrictions on learning certain portions of Torah is on Tisha B'av when we are in mourning over the descruction of the temple. Thus, it is inappropriate on Tisha B'av to study portions that make one happy.
The Jews received the Torah from God written in Hebrew, and significant numbers still read and study Torah in the original Hebrew to this day.
No. The blessing for Torah study is: Baruch atah Adonai, Eloheinu Melech haolam, asher kid'shanu b'mitzvotav v'tzivanu la'asok b'divrei Torah. Blessed are You, Adonai our G-d, Ruler of the World, who has sanctified us with your commandments and commanded us to engage in the words of Torah.
1) By maintaining yeshivot (halls of Torah-study). 2) By respecting and obeying their Torah-sages. 3) By observing the command to study and teach Torah (Deuteronomy ch.11). 4) By obedience to the Torah and the Oral tradition (Talmud). 5) By avoiding assimilation.
A yeshiva is a school where the focus is on the study of Talmud and other Torah-texts.