1. Do Muslims believe he was a Messenger of One God? YES
Belief in all of the Prophets and Messengers of God is a fundamental article of faith in Islam. Thus, believing in Prophets Adam, Jesus, Moses, and Muhammad (peace and blessings be upon them) is a requirement for anyone who calls him or herself a Muslim. A person claiming to be a Muslim who, for instance, denies the Messengership of Jesus, is not considered a Muslim.
The Quran says in reference to the status of Jesus as a Messenger:
"The Messiah (Jesus), son of Mary, was no more than a Messenger before whom many Messengers have passed away; and his mother adhered wholly to truthfulness, and they both ate food (as other mortals do). See how We make Our signs clear to them; and see where they are turning away!" (Quran 5:75).
2. Do Muslims believe he was born of a Virgin Mother? YES
Like Christians, Muslims believe Mary, Maria in Spanish, or Maryam as she is called in Arabic, was a chaste, virgin woman, who miraculously gave birth to Jesus.
"Relate in the Book the story of Mary, when she withdrew from her family, to a place in the East. She screened herself from them; then We sent to her Our spirit (angel Gabriel) and he appeared before her as a man in all respects. She said: I seek refuge from you in God Most Gracious (come not near) if you do fear God. He said: Nay, I am only a Messenger from your Lord, to announce to you the gift of a pure son. She said: How shall I have a son, when no man has ever touched me, and I am not unchaste? He said: So it will be, your Lord says: ‘That is easy for Me; and We wish to appoint him as a sign unto men and a Mercy from Us': It was a matter so decreed" (Quran 19:16-21).
3. Do Muslims believe Jesus had a miraculous birth? YES
The Quran says:
"She (Mary) said: ‘O my Lord! How shall I have a son when no man has touched me.' He (God) said: ‘So (it will be) for God creates what He wills. When He has decreed something, He says to it only: ‘Be!'- and it is" (3:47).
It should also be noted about his birth that:
"Verily, the likeness of Jesus in God's Sight is the likeness of Adam. He (God) created him from dust, then (He) said to him: ‘Be!'-and he was" (Quran 3:59).
4. Do Muslims believe Jesus spoke in the cradle? YES
"Then she (Mary) pointed to him. They said: ‘How can we talk to one who is a child in the cradle?' He (Jesus) said: ‘Verily! I am a slave of God, He has given me the Scripture and made me a Prophet; " (19:29-30).