I think perhaps it might be helpful to briefly cover what the Torah and the Talmud are.
What's the Difference Between the Torah and the Talmud?http://www.aish.com/atr/Torah_versus_Talmud.htmlThe Aish Rabbi Replies:
The first thing to know is that the Torah consists of two parts: The Written Torah, and the Oral Torah.
The Written Torah totals 24 books, including the Five Books of Moses and the prophetic writings – e.g. Isaiah, Jeremiah, Psalms, Proverbs, etc.
The Five Books of Moses – comprised of Genesis, Exodus, Leviticus, Numbers and Deuteronomy – was written down by Moses in 1273 BCE, and includes all 613 commandments (mitzvahs)....
(Jews consider it insulting to call it the Old Testament, as this implies a New Testament, which Jews reject.)...
So what is the Oral Torah? Its name derives from the fact that it was not allowed to be formally written down but had to be taught orally. It contains the explanations of the Written Torah...
In 190 CE, persecution and exile of the Jewish people threatened the proper transmission of the Oral Torah. Therefore, Rabbi Yehudah HaNasi compiled written notes on the Oral Torah called the "Mishnah" (Hebrew for "teaching")...
In 500 CE, the Jewish people again suffered an uprooting of their communities, and two Babylonian rabbis – Rav Ashi and Ravina – compiled a 60-volume record of rabbinic discussions on the Mishnah, called the "Gemara." Together, the Mishnah and Gemara comprise what is commonly called the "Talmud."
It is commonly accepted by all Jews that the Talmud or Oral Torah was codified into written form by Rabbis several hundred years following the time of Moses and the Written Torah. This has led to a schism in Judaism over the divine nature of the Oral Torah.
There are some branches of of Judaism such as Karaite Judaism which reject the Oral Torah altogether viewing it as human opinion and therefore not binding. Within Rabbinic Judaism which is far larger than Karaite Judaism disagreement remains between the Reform, Conservative, and Orthodox branches.
Below is a link to the opinion of three Rabbi's one Reform, one Conservative, and one Orthodox on the topic of whether the Talmud (written by Rabbis) carries the same divine authority at the Written Torah.
http://www.jewishvaluesonline.org/37According to this source it appears the Orthodox are most likely to hold the Talmud as divinely inspired and the Reform movement the least likely.
Regarding the content of the Talmud itself I cannot comment for I have no knowledge of the topic. However, I have never heard anyone argue that Jesus took his teachings from the Talmud. This would strike me as a hard argument to make given that the aristocratic Jewish elite at the time the Sadducees rejected the Talmud altogether. Regarding unfavorable writings by early Jewish Rabbis towards Christianity is that really a surprise?
Historic Jewish Views on Christianityhttp://www.myjewishlearning.com/article/jewish-views-on-christianity/3/ In its very earliest days, Christianity was seen by the Jewish teachers as a Jewish heresy; its adherents were Jews who believed in the divinity of Christ [and considered Christianity a Jewish sect]. But when Christianity spread and became a world religion, with numerous converts from the Gentile world, it became a rival religion to Judaism. Christians were then seen as Gentiles not because they were Christians but because, in the main, they were, in fact, Gentiles (i.e. not Jewish).
Rabbinic Attitudes
In the Talmud and midrash, the comparatively few references to Christianity (these only appear in uncensored versions) are to this religion as a heretical sect believing in a form of dualism, God the Father and God the Son... It was not until the Middle Ages that the status of Christianity (and of Islam) as a rival religion was considered from the Jewish point of view.
Medieval Attitudes
Attacks on Christian dogma are found in medieval Jewish writings from the biblical commentaries of Rashi and [David] Kimhi, refuting the Christian claim that the Old Testament contains prophesies anticipating the coming of Jesus... on the grounds that God, being God, can as little become human as He can wish Himself out of existence...
In these and similar works the main thrust was to deny that the Messiah had come in the person of Jesus (the world gave no evidence that this glorious age had arrived, it was frequently protested) and especially to take issue with the doctrine of the Incarnation and the Trinity...The medieval thinkers who held Christianity but not Islam to be an idolatrous faith did so particularly because of the worship of the Cross; to bow before an icon or a crucifix was held to be akin to bowing to idols...
Menahem Meiri [a thirteenth-century talmudist]... argued that the references to pagans in the talmudic literature could not apply to what he called “people whose lives are governed by religion.” Eventually, a distinction was made, unknown in the talmudic sources, according to which Christianity did constitute idolatry for Jews but not “for them” (i.e. Christians). A Christian did not offend against the Noahide laws [the seven principles, including the rejection of idolatry, by which Judaism expects non-Jews to live] since the Torah allows a Gentile, but not a Jew, to worship another being in addition to God.
This concept was known as shittuf (“association,” of another together with God) and the oft‑quoted legal maxim, allowing for a more liberal attitude towards Christians, is: “A Noahide is not enjoined to reject shittuf.”...
Modern Attitudes
In modern times there has been far greater cooperation between Jews and Christians, many Jews welcoming Jewish‑Christian dialogues in which the aim of each side is to understand the position of the other, and even learn from it, without in any way moving from its own. Some Jews believe that Judaism and Christianity have so much in common that it is permissible to speak of a Jewish-Christian tradition...
A single contemporary Orthodox Jewish theologian in the US has argued that Judaism does not oblige Jews to reject the doctrine of the incarnation as impossible in itself. For him, Jews reject Christianity not because God could not have become incarnate in a human being, since that would compromise God’s omnipotence, but because, in fact, He did not do so in the person of Jesus.
This eccentric view is rejected by all other Jewish theologians on the grounds that God, being God, can as little become human as He can wish Himself out of existence.
It would certainly be incorrect to say that the suspicions of the two religions of one another are a thing of the past. What can be said is that, in an age of greater religious tolerance, there has been a growing realization that the two have enough in common to enable them to work in harmony for human betterment.
Edit: Here is an interesting little video that goes over the differences between Rabbinic and Karaite Judaism
https://www.youtube.com/watch?v=iRb7DhWS6Z8&list=PLhG1viERKhXfnbaJp2JlphCVX3OvewpFp