Atheists can deny gods, but we can't "negate" them. If there's a god here somewhere, it's there, and all the disbelief in the world won't destroy it. If there aren't any gods, however, all the belief in the world won't create one.
I've addressed a lot of your numbered points before if you want to have a look in Recent Posts, but I'll summarise for you.
1. The Big Bang wasn't necessarily something coming from nothing. It might have been, sure, but nothing prevents the existence of a natural precursor: say, another universe. In that case, the implication is an infinite series of universes, or a stable external universe producing unstable internal universes like this one.
Your solution to the same problem is that God created the universe, and he existed forever before that. If you can simply declare this, isn't it simpler to cut out the extra entity and suppose that the universe itself has always existed in some form? God explanations always look so clean and simple, until you then have to explain the god.
2. Name one actually irreducibly complex system. Those presented in public so far have been hypothetically reduced, and in most or all cases already had been when they were presented as irreducibly complex. If you have a favourite example, we can go through it here.
3. The mathematical refutations of abiogenesis (life from non-life) have themselves been refuted, starting with Hoyle's famous Boeing 747 argument. In brief, although the chances were small, the opportunities were many and the possible forms early life could have taken were almost infinite. Most impossible-looking probabilities suppose that only a particular protein or enzyme must be formed.
4. Quote-mining Dawkins, of all people, will get you nowhere. The Cambrian "explosion" was if anything a very slow explosion, occurring over several million of the 15 million years of the Cambrian period. It was indeed a period of great change and many new variations, but since it's around the period when animals themselves first appeared, one would expect this. Nobody said evolution had to proceed at the same rate throughout its 3.5 billion year history.
5. The incomplete fossil record is hardly a secret. A given plant or animal has an incredibly small chance of becoming a fossil at all, and we'll never find most of them anyway, so it's inconceivable that the record will ever be "complete".
Those fossils we have found, however, paint a sparse but consistent impression of branching descent from a common ancestor. What would really throw evolutionary theory off is not missing fossils, but fossils in the wrong period. The famous hypothetical example is rabbits in the pre-Cambrian.
6. The anthropic principle is often very atheistic in nature. It counters the sense of privilege we might feel in having a planet which is perfect for our needs, by saying that we could only have emerged on such a planet, wherever it was.
What you really mean is the fine-tuning argument, which states that if the conditions of the universe were even slightly different, we could not exist. In the hypothetical context of a multiverse the above applies again; out of the many different universes we could only have emerged in one which suits our needs.
There are other objections which do not require this model, for example: perhaps to achieve a different but life-friendly universe, the conditions of the universe need to be wrenched rather than tweaked, and other equilibria exist far away from the current "settings". All possible arrangements have not been tested, only those near ours.
7. The mind can be easily explained, at least in broad strokes, by evolution. The mind is beneficial. Those animals including primates which developed rudimentary versions of the brain functions we think of as "mind" had a tremendous mental advantage over those which didn't. Later, any deadly contest of will or wits was won by whoever had the better mind. Natural selection favours the clever, all other things being equal.
8. Darwin was in no doubt that an undirected system had in fact produced the brain. It may not in fact be capable of determining ultimate truth, whatever that is, but it is perfectly capable of making reasoned decisions based on the evidence before it.
9. Perhaps nothing is intrinsically "right" or "wrong". We can never know. Therefore we adopt a heuristic approach to morality: that which is beneficial is usually right, and that which is harmful is usually wrong. If it works, we keep it. If it doesn't, we change it.
Without something transcendent to ourselves there is probably no absolute morality, but there is plenty of objective morality. The objects used can be simple and straightforward, like a comparison of relative benefit and harm, or they can be tried and tested, like the ancient ethic of reciprocity (the Golden Rule), or they can be complex and careful, like the law.
These objects can certainly be challenged, but in the absence of any infallible authority we actually know exists, we use the most solid things we have, such as logic, mathematics, group consensus and our common human empathy.
Tom, I notice something about your perspective, based on your nine issues. It is not science that points to God, it is rather the perceived failings of science. You point in every case to what science supposedly can't explain (though in most of these cases it's well on the way), instead of what it can. Yours seems to be a god of the gaps.
Those gaps are getting smaller. Just this year, for instance, scientists discovered a method by which RNA (a precursor to DNA) can form, and elsewhere they synthesised rudimentary self-replicators. There is now less we don't know about the natural emergence of life from non-life than there was a year ago. God is a necessary part of that process to fewer people. The nature of gods of the gaps, Tom, is that they shrink.
If you want to keep believing, you're better off embracing the world as it really is, rather than denying things like evolution for which the evidence is overwhelming. God can always fit around science if you want Him to. Just accept that things are as they are, and say God made them that way.
For the sake of the discussion, did God cause himself to exist? Is that not absurd too? Has he reached heat death?
If the universe has existed forever, it's an isolated, closed system by definition (since there's nothing which is not within it) so it can break even. If it hasn't always existed, why can't something simpler than a god have brought it about? Why do you discount simpler matter or energy reactions, or a previous universe, and jump straight to a fully formed, sourceless intelligence? He's even harder to explain than the universe is.
In general, why don't you apply your questions on the origin of the universe to the origin of God? Is it just a no-go zone?
Jumping to evolution, it does represent a decrease in local entropy. So does building a tower out of Lego: There was no order to the blocks, and now there is some. Would you say it's impossible to build Lego structures, or indeed to build anything at all from unordered pieces? Of course not. You think God did just that.
The key word here is "local". Within a system, entropy can decrease in one area if it increases by at least that much elsewhere. In the case of the Lego, entropy increases in your body as food is dissolved and digested. This gives you the energy to move the blocks.
So a transfer of energy can decrease local entropy enough to create order and complexity. The ultimate energy source for evolution, like nearly all earthly processes, is the sun. Earth's isolated system must of course include the sun. Its explosive fusion reactions increase entropy far more than the natural process of evolution decreases it, so no laws of physics are broken.
Thermodynamics and evolution are perfectly compatible, or else evolution would have been struck down in Darwin's lifetime; research towards entropic principles began around 1803.
So that's why we've heard the Argument from Thermodynamics a lot and yet we're still atheists.