W H A T ..... I F ..... mmmm .... there were no Gods !!
Let's say, science one day proved to complete certainty beyond any doubt that there are no Gods .. none.
What would this world look like?
More chaos or less ?
More wars or less ?
10 commandments / values / moralities?
Purposeful or meaningless life ?
Reasons to live or die?
Reasons to construct or destruct ?
More greed or more poverty?
What does it all mean ?
What would change ?
Your questions are difficult to answer for a number of reasons. First, you can't just broadly paint all religions together. A Wiccan actually has zero in common with the Christian worldview, for instance. Also, some people that practice religions are actually atheists, like some Buddhists (I guess in that case, it would be considered more of a religious philosophy). I think we might be able to say, for instance, that if Islam were banned, we might have less wars. But if Buddhism was banned, would we have less wars? I doubt anything would really change. So your questions are unfair in that respect.
However, we do have some indicators as to what a world without any inkling of God would look like. We have the Soviet Union and Pol Pot's regime. These were both states that completely destroyed or attempted to destroy belief in God. As a direct result of their Atheist philosophy, in these countries, the State became God. The result is the death of millions and millions of people due to murder, starvation, etc. Please note that this is a DIRECT result of atheist philosophy. God does not exist...therefore...and those were the results. I am not saying here that Atheists cannot be good people or that there is anything to fear from an Atheist, I'm simply pointing to an answer for your question.
Finally, if science proved that God does not exist (strange since at present the evidence points to the fact that God exists), we would at last know that objective moral values and duties are a figment of our imagination, since without a God, objective moral values and duties cannot exist (lots of Atheists believe this, like Nietzsche for instance). Once we know that objective moral values and duties do not exist, then people can determine what their own subjective morals are according to their desires. They would then be perfectly justified if they wished to rape, murder, kill, etc. What would it matter, anyways, since we are just walking bags of genetic material? Whoever would be tougher and fitter, would be stronger and survive. There would be no more need for such illusory concepts as morals anymore.