Do Muslims need to know the "Jewish Messiah"?
First of all as 'Isa/Jesus () has been sent long before Muhammad () there's no reason for Muslims to know the "Jewish Messiah" ... especially not from Jewish scripture. Muslims are more interested to know him as a messenger of Allah and that is how he is described in the Qur'an, where he also has been called "The Messiah 'Isa son of Mariam (Marry)". And therefore the Qur'an only mentioned that he came with the proofs (prophecies) without explicitly telling what these proofs are.
What sources Muslims use to get to know about Jesus/'Isa()?
The Qur'an tells the Muslim all they need to know about 'Isa () and Muslims beside this are allowed to seek knowledge of anything of what they may find in the teachings of the people of the book (Jews and Christians in first place), but they must check whether or not it is in opposition to what they have learnt in the Qur'an and (sahih/sound) sunnah as Muslims are thought that their books are corrupted.
Does the Qur'an cite passages from the Old and/or New Testament?
In first place the Qur'an denies the idea that Muhammad () has been taught by a Jew or Christian and therefore the Qur'an is considered as a divine scripture. Historical facts actually confirm this while Muhammad () was in Mekka many verses that have been revealed where discussing Jewish and Christian traditions, and in Mekka Jews were rather unknown and Christians who didn't convert were too few to have any influence and no historian came with a name of a teacher.
The Qur'an actually might cite passages which sound similar to what is written in the Old testament, but investigating which and where and to what extent there's an accordance is neither the topic of this site nor something Muslims and Muslim scholars primarily cared about, even if there are certainly some contributions in this matter. For example some scholars like ibn Hazm have discussed false believes or errors in the believes of all kinds of sects and religions (including some Muslim sects) and some scholars of tafseer (exegesis of the Qur'an) have quoted a few links to the Old and New Testament in their works among them sheikh Taher ibn 'Ashur.
Some examples can be found in:
What does the Qur'an say about Jesus/'Isa ()?
The Qur'an informs Muslims that 'Isa () has been born by a divine "order" (be and he was) and his mother Mariam () became pregnant and that she fasted (by not speaking) and he 'Isa() the baby answered instead of her. The Qur'an also emphasizes on the fact that he is a messenger not a deity and that he was the Messiah sent to the sons of Israel. The Qur'an tells us about some miracles like:
- his creation which was similar to that of Adam ().
- being able to speak from the cradle on.
- being supported by the pure spirit.
- forming from clay something having the form of a bird making it a bird with Allah's permission.
- healing the blind and the leper with Allah's permission.
- and bringing back to live dead people with Allah's permission.
The Qur'an moreover quote the difficulties and resistance he found in his preaching and that he cursed his enemies. It also quotes the fact that his enemies pretended him to apply magic and that they pretended having killed him after he was raised by Allah. It also quotes that he was raised alive and leaves the impression that he might come back. The Qur'an also quotes the story of the table (al-Maidah) which was a (little) miracle for his followers. And that 'Isa told his followers and the sons of Israel that he will be followed by a messenger called Ahmad. If I'm not wrong this is a hopefully full summary of what the Qur'an has quoted. Now I'll hopefully quote the relevant verses.
In the following I'll present a list of verses in the Qur'an quoting the word "'Isa ()" -which appears 25 times in the Qur'an- the list would be much longer if I'd quote any verse referring to him or to the Messiah son of Mary. I will try to arrange them by topic and post an example of each of them and refer to similar examples: Also for better understanding I recommend you to read these quotes in more context:
Muslims believe in Allah and all his Messengers () and Prophets () (including 'Isa())and to what was revealed to them:
Say, [O believers], "We have believed in Allah and what has been revealed to us and what has been revealed to Abraham and Ishmael and Isaac and Jacob and the Descendants and what was given to Moses and Jesus and what was given to the prophets from their Lord. We make no distinction between any of them, and we are Muslims [in submission] to Him." (2:136)
See also (3:84).
The message all Messengers () and prophets () (including Muhammad () and 'Isa ()) have preached is the same:
Indeed, We have revealed to you, [O Muhammad], as We revealed to Noah and the prophets after him. And we revealed to Abraham, Ishmael, Isaac, Jacob, the Descendants, Jesus, Job, Jonah, Aaron, and Solomon, and to David We gave the book [of Psalms]. (4:163)
See also (42:13).
'Isa came confirming what was in the Torah and with some new rulings and revelation:
And We sent, following in their footsteps, Jesus, the son of Mary, confirming that which came before him in the Torah; and We gave him the Gospel, in which was guidance and light and confirming that which preceded it of the Torah as guidance and instruction for the righteous. (5:46)
See also (57:27) which describes his followers too and (43:63) which make clear that 'Isa came to correct false interpretations and solve disputes about the interpretation of the Torah. And also What specifically does Jesus make lawful in Qur'an 3:50?.
He also announced that he will be followed by Muhammad ():
And [mention] when Jesus, the son of Mary, said, "O children of Israel, indeed I am the messenger of Allah to you confirming what came before me of the Torah and bringing good tidings of a messenger to come after me, whose name is Ahmad." But when he came to them with clear evidences, they said, "This is obvious magic." (61:6)
He was given clear proofs to show he is the Messiah, but was rejected and called a magician by his enemies:
And We did certainly give Moses the Torah and followed up after him with messengers. And We gave Jesus, the son of Mary, clear proofs and supported him with the Pure Spirit. But is it [not] that every time a messenger came to you, [O Children of Israel], with what your souls did not desire, you were arrogant? And a party [of messengers] you denied and another party you killed. (2:87)
See also (2:253) emphasizing on the dispute about him (6:85)
His creation was like that of Adam ():
Indeed, the example of Jesus to Allah is like that of Adam. He created Him from dust; then He said to him, "Be," and he was. (3:59)
The good tidings of his birth:
[And mention] when the angels said, "O Mary, indeed Allah gives you good tidings of a word from Him, whose name will be the Messiah, Jesus, the son of Mary - distinguished in this world and the Hereafter and among those brought near [to Allah ]. (3:45)
Some of the gifts and miracles Allah gave him:
[The Day] when Allah will say, "O Jesus, Son of Mary, remember My favor upon you and upon your mother when I supported you with the Pure Spirit and you spoke to the people in the cradle and in maturity; and [remember] when I taught you writing and wisdom and the Torah and the Gospel; and when you designed from clay [what was] like the form of a bird with My permission, then you breathed into it, and it became a bird with My permission; and you healed the blind and the leper with My permission; and when you brought forth the dead with My permission; and when I restrained the Children of Israel from [killing] you when you came to them with clear proofs and those who disbelieved among them said, "This is not but obvious magic." (5:110)
See also Which disease did 'Isa cure?
It is false to claim 'Isa () or his mother is anything else than a human and 'Isa () himself denied having pretended this:
O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was but a messenger of Allah and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allah and His messengers. And do not say, "Three"; desist - it is better for you. Indeed, Allah is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allah as Disposer of affairs. (4:171)
See also (5:116) and Surah Al- Maa'idah, ayat 75.
The story of the table:
[And remember] when the disciples said, "O Jesus, Son of Mary, can your Lord send down to us a table [spread with food] from the heaven? [Jesus] said," Fear Allah , if you should be believers." (5:112)
And in (5:114) his supplication of Allah asking him to give them what they asked for is mentioned.
When 'Isa () found persistence and disbelief from the sons of Israel he asked why are my supporters for the cause of Allah and the disciples answered and said they are supporters for Allah (Muslims):
But when Jesus felt [persistence in] disbelief from them, he said, "Who are my supporters for [the cause of] Allah ?" The disciples said," We are supporters for Allah . We have believed in Allah and testify that we are Muslims [submitting to Him]. (3:52)
See also in (61:14).
'Isa cursed his enemies from among the sons of Israel:
Cursed were those who disbelieved among the Children of Israel by the tongue of David and of Jesus, the son of Mary. That was because they disobeyed and [habitually] transgressed. (5:78)
Allah has raised and purified him and didn't leave him get crucified by his enemies:
[Mention] when Allah said, "O Jesus, indeed I will take you and raise you to Myself and purify you from those who disbelieve and make those who follow you [in submission to Allah alone] superior to those who disbelieve until the Day of Resurrection. Then to Me is your return, and I will judge between you concerning that in which you used to differ. (3:55)
See also Did prophet 'Isa go to the cross? and Surat Al `Imran 3/55 about the death of Jesus(puh)
Allah denies that Jews have killed him:
And [for] their saying, "Indeed, we have killed the Messiah, Jesus, the son of Mary, the messenger of Allah ." And they did not kill him, nor did they crucify him; but [another] was made to resemble him to them. And indeed, those who differ over it are in doubt about it. They have no knowledge of it except the following of assumption. And they did not kill him, for certain. (4:157)
Allah shows that the people of the book have a dispute about him:
That is Jesus, the son of Mary - the word of truth about which they are in dispute. (19:34)
Allah informs that He took a solemn covenant from all his prophets ()
And [mention, O Muhammad], when We took from the prophets their covenant and from you and from Noah and Abraham and Moses and Jesus, the son of Mary; and We took from them a solemn covenant. (33:7)
I want to repeat my recommendation from above of reading these verses in more context as the story of 'Isa () is not covered in the quotes and links above only, but also in the verses in between, especially in surah 5: al-Maidah.
Note the Qur'an also tells the story of Mariam/Mary () the mother of 'Isa () -read for example the first part of Surah 19: Mariam (Mary)- etc. which might also reveal some relevant information on this topic beside including some compliance with the New Testament.
Some relevant posts: