Biblical inerrancy and biblical literalism is a Protestant tradition. These days, most likely a fundamentalist Protestant tradition.
Fundamentalist Protestants are only a minority of world Christianity.
Whether or not the bible is divinely inspired is the realm of opinion. I don't think a guy in a white robe was telling Luke what to write.
Disagreement on the day Jesus died seems pretty minor to me. All the authors in the NT seem to convey a Jesus who preached universal love, mercy, and stood on the side of the poor and oppressed. That essence seems authentic, given that multiple independent sources convey it.
Very little ancient literature that survives records events in real time as events unfolded. The lives and teachings of Confucius and Bhudda were written down centuries after they died. The Histories of Herodotus were written decades after the Greco-Persian wars. Are historical sources for the Mauryan Empire of India post-date the empire by centuries. No writings of the Greek Ionian philosophers survive. We only know about them by the writings of Athenian Greeks more than a century later.
Saint Paul knew at least two of Jesus' disciples, Peter and Jesus' brother James. Some people think Mark was Peter's companion and Mark's Gospel in a summary of what Peter told him. That is open to debate. As far as surviving ancient sources though, that is pretty decent at getting back to original sources.