No. According to evidence that we now have, most Biblical scholars believe that Jesus was born in 4 BCE, not 1 CE. Although, admittedly the Julian Calendar still would have failed to get the date right. The Romans simply miscalculated.
Whether or not Jesus was actually the Jewish Messiah is not universally agreed upon. While Christians assert that he is, Jews do not believe this. Muslims, while calling Jesus "the Messiah" have a very interpretation of this term.
Christians believe that Jesus was the Jewish Messiah. Jews disagree.
Jesus' birthday is not marked in the Jewish calendar.
The calendar is intended to mark the number of years since the death of King Herod the Great. The Roman abbot Dionysus Exiguus devised the new Christian calendar in 533. He knew that it was impossible to say when Jesus was born, but he knew, or thought he knew, when Herod died. So, he chose to begin his Christian calendar on the year of Herod's death, and he based this on the reign of the Roman emperor Augustus. Unaware that Augustus only adopted that name four years after his reign began, going by his birth name of Octavius until then, Exiguus commenced his calendar just 4 years too late.
The Jews do not recognize Jesus of Nazareth as the Messiah, they are still waiting for the Messiah to come.
No, Jesus did not invent the calendar. The modern calendar system in use today (the Gregorian calendar) was created centuries after Jesus' time, in the 16th century. It is based on the solar calendar introduced by Julius Caesar in 45 BCE.
B.c
The Jews do not recognize Jesus as the Messiah.
Judaism does not feel that Jesus fulfilled any part of the role of the Jewish Messiah. It is Christianity and Islam that assert that he did.
The vast majority of Jewish people do not believe that Jesus was the messiah, but that the messiah has yet to come.
There is no month of Nisan in the Gregorian calendar.
Many believe Jesus was born around December 25. However, the Bible does not give his date of birth, only the date of his death, Jewish calendar month of Nisan, Gregorian calendar March/April. However, we know that Jesus was about 33 1/2 years old when he died, so his birth would have been sometime in the autumn, around October. As important as it was for the Messiah to come to Earth, the focus is on his death. Because by means of it, we may live. (John 3:16)
The Julian calendar was in place then. It preceded the Gregorian calendar that we now use. Like the Gregorian calendar, the Julian calendar had 365 days, with a leap year of 366 days. There is only a slight difference of a few minutes between the precise length of the Julian calendar and the Gregorian calendar. <<>> The Julian calendar has a leap year every 4 years, with an average year of 365.25 days. The Gregorian calendar we use now has 97 leap years in every 400 years, so the average year is 365.2425 days.