I can answer the question posed in the title of my post in one word: No. Many people think that Christians stole ideas from Zoroaster thereby mythologizing Jesus. There are several problems with this view. The first problem has to do with dating and with sources of information we have regarding Zoroaster himself. The second problem is that Zoroaster's life that we have documented does not parallel Jesus.
There are several opinions when Zoroaster lived and when the religion started. Some say 6000 BCE or 600 BCE. For the sake of argument lets take 600 BCE, arising from Persia. The earliest written records we have were written down between 6th-9th centuries C.E. Adherents (yes, there are still follower s of Zoroaster today) believe that Zoroaster himself lived 1500 - 1000 BCE. In other words, no one is really sure when Zoroaster lived. Therefore for the majority of the time the religion has been practices it's been based on oral stories before being written down. The time scale between the time Zoroaster actually lived and his stories written down is extremely large compared to Jesus and the New Testament, no matter how late you want to date any book in the New Testament. Of course myth and legend must have clear crept into Zoroastrianism during 2000 years. Not to mention it is far more likely Judaism influenced Zoroastrianism rather than the other way around since Judaism came first. In contrast we can date the creed from 1st Corinthians 15 to just a few years after Jesus' crucifixion that most historians agree really happen. And if you reject that argument you still have to admit that the creed found in 1st Corinthians 15 is from the 50's or 60's CE and that Christians had been teaching the death, burial, and resurrection of Jesus since Christianity's earliest days, proving that the belief did not come from legend based on people who were not eyewitnesses.
I found a link that lists common alleged parallels between Zoroaster and Jesus and discusses if they hold up or not. I've pasted it below so you can see it here.
1. Zoroaster was born of a virgin and "immaculate conception by a ray of divine reason."Any honest person would have to agree that Zoroaster does not equal Jesus Christ. They are too different. Here are some more sources
Zoroaster's mom was married when she gave birth to him, and there's nothing suggesting she was celibate while married. The "ray of divine reason" was apparently a purely spiritual thing, and Zoroaster's body actually was created the usual way.
2. He was baptized in a river.
Zoroaster receives a revelation while on the banks of a river. That's the closest parallel to be found.
3. In his youth he astounded wise men with his wisdom.
Sort of. At age 7, he was put under the care of magi, who he frequently argued with. Later, the magi had him imprisoned, but he was freed after he made the legs grow back on a horse.
4. He was tempted in the wilderness by the devil.
There is a parallel in the Zoroaster story to Jesus' temptation, and, yes, it does apparently predate the Jesus story by a couple hundred years. However, Zoroaster's "temptation" wasn't by the "devil" (in Zoroastrian literature, Ahriman) and it may or may not have been in the wilderness (the texts don't say). Zoroaster is tempted by a demon, not by Ahriman himself. And his temptation doesn't involve turning stones to bread or leaping from towers, just dialogue between Zoroaster and the demon.
5. He began his ministry at age 30.
True, but the earliest reference to his being thirty is post-Christian.
6. Zoroaster baptized with water, fire, and "holy wind."
First of all, there's no reference to Zoroaster baptizing with any of these things. Second of all, there's no Biblical reference to Jesus baptizing with any of these things! Is the fact that neither of them do these things a parallel?
7. He cast out demons and restored the sight to a blind man.
There's no reference to Zoroaster casting out demons, and the earliest reference to his giving eyesight to the blind is from the 10th century A.D.
8. He taught about heaven and hell, and revealed mysteries, including resurrection, judgment, salvation and the apocalypse.
Zoroaster did teach about heaven and hell, and resurrection into a non-dying body. Judgment is done by other gods, but with Zoroaster pleading the case of those who are faithful to him, though, unlike with Christianity, the faithful are not automatically saved. Salvation is achieved by works alone, unlike Christianity. And the apocalypse Zoroaster spoke of was a flood of molten metal. Sounds like a pretty good comparison, huh? However, most of this is from post-Christian writings. Also, most of these subjects begin on the Bible's Old Testament, which predates the earliest Zoroastrian references by several hundred years.
9. He had a sacred cup or grail.
First of all, Zoroaster did not have a sacred cup or grail. Second of all, Jesus (at least according to the Bible) did not have a sacred cup or grail. The Christian "holy grail" is believed by some to be the cup Jesus drank from at the last supper, and others say it was a chalice that collected Jesus' blood at the crucifixion. But as far as its being 'sacred', the Bible makes no such claim. This is a medieval non-Biblical legend.
10. He was slain.
Ummm...okay. So were Caesar, Abraham Lincoln and John Dillinger. Is this supposed to be significant? Let's look at how Zoroaster was slain and see if there is any comparison to how Jesus was slain, shall we? One story has him murdered at the age of 77 by a wizard. Another has him killed in battle. Both of these stories date from the 15th century at the earliest.
11. His religion had a eucharist.
Since they believe in salvation by works alone, why would they have a eucharist? The closest thing they have to a eucharist is a ritual involving the haoma plant, but they don't claim the plant is Zoroaster's body or blood. Besides, the earliest reference to this ritual is post-Christian.
12. He was the "Word made flesh."
No reference to this, implicit or explicit.
13. Zoroaster's followers expect a "second coming" in the virgin-born Saoshyant or Savior, who is to come in 2341 CE and begin his ministry at age 30, ushering in a golden age.
First, there's nothing about his being thirty, or of the redeemer being Zoroaster himself. Even the religion disagrees with itself on exactly what's going to happen, though the date of 2341 CE is given (although how this date compares to Jesus, I have no idea). A pre-Christian text (around 400 B.C.) refers to a single redeemer who ushers in a golden age. Later post-Christian texts suggest there will be three redeemers conceived by virgins who bathe in a lake in which Zoroaster's sperm is being divinely preserved. One of these redeemers will eradicate death. Only the one pre-Christian reference could be considered valid, but that one mentions nothing about the return of Zoroaster himself or virgin birth.
Was Jesus Zoroaster or Buddah? - This ia good article however the author rejects Jesus and Christianity, however, great information on Buddha and Zoroaster.
Zoroaster - Wikipedia
Aren’t there some striking parallels between the Jesus and Zoroaster stories?