"The Bible says literally nothing about the laws of logic, and the rules in the Bible are one particular set of rules. Does that mean they are rules that everybody should follow?"
It doesn't say anything that I know of, but my point is a naturalistic worldview can't explain abstracts like logic and morals. And the rules in the Bible are for morals so yes everyone should follow them.
"Criticizing the Big Bang for not explaining morality and logic is like criticizing oceanography for not explaining the formation of stars and planets. It's a completely different field of study."
I just used the Big Bang as an example, but the point still stands that naturalism can't explain logic and morality. Where do you think the laws of logic and morality came from?
"If the Bible explains morality so well, do you think all the rules in the Bible are rules we should follow today?"
They are the rules for morality so yes.