Please provide proof that radio-carbon dating is accurate and trustworthy.
That's what universities, textbooks, popular science books, and the Internet are for. You are responsible for your own education, just as those you ask were responsible for theirs. Unless you're a young person, if you still don't know about radiometric dating, it's because you've never had an interest in it. That doesn't usually change, but if it does, you know where to go. You've already been offered a link on the topic. Did you look at it? (rhetorical question).
This is what I call the creationist two-step. Think Charlie Brown, Lucy, and the football. Over and over, the apologist asks for information that he has no interest in and never looks at. Why? I presume it is to try to represent an interest in scholarship and critical thinking where there is none. Or maybe it's an attempt at an argument from ignorance: if you can't make me understand, you're wrong, therefore God.
Whatever the answer, not once have I seen one of these encounters result in a theist reviewing the material offered and returning to the thread to discuss it. Not once.
No one has shown real flaw in the Bible, only in their opinions/interpretations and how they feel it should be.
Not to you, they haven't, but they have to many others.
And this is why I believe Bible is done with the guidance of God. If it would be just from humans, atheists would not have so many problems to understand it and they could show real errors in it, instead of dishonest interpretations and straw man arguments.
Atheists have no problem understanding the Bible? Why would they? It's simple language. Vague, and ambiguous, yes, meaning that much of it has no definite meaning, but it doesn't take much expertise to recognize that.
It's very easy to demonstrate the errors in the Bible to anybody that doesn't have a vested interest in believing it is error-free. Those wearing a faith-based confirmation bias are the only ones unable to see those errors - internal contradiction, errors in history and science, failed prophecies and other unkept promises, moral and intellectual failures attributed to a god called perfect. I won't trouble you with examples for obvious reasons.
The theory of evolution can't be proven correct with scientific method.
The theory is correct. It meets the legal burden of proof - shown likely to be true beyond a reasonable doubt, and the theory met that standard long ago. The only other logical possibility is a deceptive, superhuman intelligent designer that stocked the earth with findings intended to make it look like evolution had occurred, and that's pretty far-fetched (not a reasonable doubt). Think about it: What if the theory were falsified tomorrow? How would we then understand those mountains of earlier data in the light of the falsifying finding?