The big bang is still a theory. We know a lot about the theory....but we don't know if it actually happened or not, so effectively we don't know much.
Yes, however we know so much about the natural world and history to ascertain that the veracity of the Bible is non-existent. The writers of both testaments are unaware of basic scientific realities, assert that the entirety of the human race was populated by two people in Mesapotamia, that the Jews escaped from Egypt, which never happened, and all kinds of other bullshit.
You cannot disprove God, as a concept, however there is not a single shred of evidence to suggest that he exists, so it is not illogical to assert he doesn't. If there is no evidence to suggest something exists, it is an entirely logical assertion to say that it probably doesn't.
However we can absolutely disprove the Bible. To get to the point that the idea of God is not intellectually absurd and childish, you need to begin to deal with an entirely more vague and un-Biblical conception of God.
The Bible says God created the universe in 6 days. In other places in the Bible it hints that God is outside out concept of time, and a blink of an eye to God is like 1,000 years. That is where some get the 6,000 year creation from, but I think that the Bible is trying to be more general.
No, the Bible is extremely specific and not at all intended to be general. This is just an excuse made by modern Christians when they realise that the Biblical account doesn't hold a candle to the scientific understanding of the universe of a modern 13 year old.
I think the creation time period is not specified, rather the six days represent six stages of creation. And science supports this.
Science shows this is directly and entirely wrong.
Genesis asserts that there was 'light' ("night and day") before the Sun even came into existence. This is naturally impossible. The Bible also asserts that plants began to grow before there was sunlight and that every plant and tree which yield seed are given to us by God as good to eat.
It also asserts that a fucking snake can talk, for goodness sake.
That is where some get the 6,000 year creation from
Not at all. This was derived from counting down the generations and ages described in the Bible of early humanity by historians and chronologists in the late dark ages.