Nobody, generally, dates Jesus' birth to 0 CE. Dionysius Exiguus erred in his calculations, or at least failed to reckon correctly, so that the actual date of a historical Jesus figure would be in the range 4-6 BCE. 4 BCE is the latest date normally considered, because we can fix the date of Herod the Great's death, and those christian documents that narrate Jesus' birth all place it in the time of Herod the Great. Hence, Herod must still be alive.

That Jesus was a historical figure is generally accepted. See the faq, including my answer, for a longer treatment of this topic.

There isn't a lot of agreement, let alone consensus, about the historical Jesus, beyond his birth and the fact of his crucifixion, but it is generally accepted that he died, and via crucifixion. The year of his death is usually considered to be either 30 CE, or 33 CE. I would have to dig through some notes to go over the case for these dates, but I prefer 33 CE as more likely.