How do we "know" that the Torah was given by G-d at Sinai and not man-made? And even if it was given by G-d, how do we know that all the teachings ascribed to the Torah were given by G-d as opposed to the rabbis having made much of it up?
Regarding your first question, the author of Kuzari, Rabbi Yehuda HaLevi, presents what is often called "The Kuzari Principle". The argument goes as follows: Judaism's claim to truth is that, unlike the claims of any other religion, G-d appeared to an entire nation, revealing His will that they fulfill a most exacting system of beliefs and practices. Since the entire religion is predicated on this mass-revelation, no one could ever convince an entire nation to accept the religion based on a purported experience that no one ever had.
Simply put, if mass-revelation never happened, no one could ever use it to convince others that it did. This is certainly true if the fabrication was directed to that generation itself, since no one could convince others that they experienced something they didn't. But it's even true if the claim was made regarding the experience of an earlier generation. Because if it was purported to have happened to the nation's forefathers, why didn't anyone ever hear of it?
This is a sound basis for the premise that G-d gave Torah to Israelat Sinai. But you ask, how do we know that the Torah that we have is what G-d gave? Maybe the rabbis added to it in G-d's name.
To this I would offer two replies:
First, the religious leaders in all times, such as the prophets or the Sages of the Talmud, were G-d fearing people who revered the Torah and dedicated their lives to preserving its integrity. In addition, given their great and numerous teachings demanding impeccable ethical standards in general, and in particular extolling truth and abhorring falsehood, it is nearly unthinkable that they would intentionally falsify the Torah, clothing their own agenda in the mantle of G-d.
Second, the Talmud, for example, goes to great lengths to painstakingly differentiate between Torah Law and rabbinical legislation. It is true that the Talmud invokes the authority to add laws and customs from Torah verses, and often seeks Torah-basis for these decrees, but it always clearly demarcates the distinction between what's from the Torah and what is from the prophets or Sages. So rather than falsely presenting their legislation as Torah, we find that the Rabbis actually stress the difference between theirs and that of the Torah.
These are some of the major reasons why the Torah as explicated by the Talmud is considered the True Torah.