First of all, I'm an agnostic (basically means I have no idea...I'm not saying that there is or isn't a god).
1) The current theory about the Big Bang doesn't say that there is "an eternity of the past of cause and effect"...on the contrary, causality breaks down at the moment of big bang: all the matter in the universe was concentrated in a singularity, so if there was anything before that it had no effect on anything after the big bang.
Unless you take the Bible too literally, the Big Band doesn't contradict it

2) No one is saying that the Big Bang (or any thing else) happened by itself. The Big Bang is a theory that takes into account actual evidence, that's it.

3) Trying to disprove something that by definition doesn't have any proof of existing is hard and pointless. That's what I don't like atheists that refuse to consider the existence of a god.

4) This is basically just point 1) again, I think