1) Rabbi means 'my master', an honorific title for a teacher, like a Ph.D. This is evident from Jesus' use of it in Matthew 23.
History
The rabbi is not an occupation found in the Torah (Five books of Moses); the first time this word is mentioned is in the Mishnah [dating from around 80CE]. The modern form of the rabbi developed in the Talmudic era. Rabbis are given authority to make interpretations of Jewish law and custom.
Rabbi is a Hebrew term used as a title for those who are distinguished for learning, who are the authoritative teachers of the Law, and who are the appointed spiritual heads of the community. The word Rabbi is derived from the Hebrew word RV, which in biblical Hebrew means "great" or "distinguished,". In the ancient Judean schools the sages were addressed as "Rabbi" (my master). This term of respectful address gradually came to be used as a title, the pronominal suffix "i" (my) losing its significance with the frequent use of the term. - Websters Online
And according to
the JewishEncyclopedia:
The title 'Rabbi' is borne by the sages of Palestine, who were ordained there by the Sanhedrin in accordance with the custom handed down by the elders, and were denominated 'Rabbi,' and received authority to judge penal cases
Jesus was not ordained by anyone but God. Not even the great leader of the Sanhedrin,
Hillel, was called "rabbi" (he presided during the reign of Herod the Great (37-4 BC)):
The more ancient generations, however, which were far superior, had no such titles as 'Rabban,' 'Rabbi,' or 'Rab,' for either the Babylonian or Palestinian sages. This is evident from the fact that Hillel I., who came from Babylon, had not the title 'Rabban' prefixed to his name.
Wherever Jesus received his authority from, it was not from the Sanhedrin. That he was called rabbi at all, means that his disciples recognized him as an authority higher than the ordained Pharisees. That would have excited them no end
.
Ironically, what you know of rabbi's today probably comes from Christian tradition:
As a matter of course, the example of the minister in the Church, especially in Protestant countries, exerted a great influence upon the function and position of the rabbi in the Synagogue; even upon his outward appearance, since the vestments of the Christian clergy, or their abandonment, have sometimes been copied by the modern rabbi...
Another function of the modern rabbi which follows the pastoral practise of the Christian minister is the offering of consolation and sympathy to persons or families in bereavement and distress, in forms perhaps more cheering and elevating than those formerly in use. Here, as well as in his pulpit and educational work, the modern rabbi has the opportunity of bringing the blessings of religion home to every individual in need of spiritual uplifting. - JE: Rabbi
2) 'Original sin' is a misnomer. But it comes down to this:
1 John 1:8
If we claim to be without sin, we deceive ourselves and the truth is not in us.
As for what Jews believe: "
There is no man that sinneth not" (I Kings viii. 46); "
For there is not a just man upon earth, that doeth good, and sinneth not" (Eccl. vii. 20; see Sanh. 105a).
On the other hand, it is maintained that at least four persons—Benjamin, Amram, Jesse, and Chileab—died without having committed any sin and merely as the result of Adam's weakness in yielding to the temptation of the serpent. - JewishEncyclopedia: Sin
Make of that what you will.