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.
From the development of the eye to the beauty of a waterfall to the exact value of the gravitational constant, theists may claim that anything natural with any quality to it whatsoever must have been deliberately crafted with humanity in mind. This is the Argument from Design.
Even if it were correct, it's a terribly egotistical way of looking at the world. And even if it were proven to be correct, no religion would have any basis upon which to claim that the designer or creator was its particular god or gods.
The basic answer to the argument from design is that there is no substantive evidence for it and therefore 1. to assume design in the presence of alternative theories supported by substantive evidence is putting one's head in the sand and 2. to assume design even in the complete absence of alternative theories is an argument from ignorance.
Beginning with evolution and the development of intelligent humans, there is a huge amount of geological, genetic and observed evidence to support the currently held view of the "tree of life". Evolution of subspecies is observed all the time, and contrary to a common objection whole new species have been seen to emerge, and recently. (This article on speciation has some examples.)
Contrary to another creationist talking point, there are tons of known transitional fossils. Contrary to Kirk Cameron, these don't look like half of one animal joined to half of another (like his famous Croco-duck). They're more like what you get if you morph a whole picture of one into a picture of the other, but stop halfway.
To dismiss evolution as a useless series of random changes is an argument from personal incredulity, which is a type of argument from ignorance. It's also wrong. The mutations are random, but only the beneficial mutations tend to be passed on by sheer survival and procreation skills. Evolution doesn't just try random things and get it right every time, it tries everything and goes with what works. It's like trying to hit a dartboard by spraying the whole wall with a machine gun. You'll miss a lot, but you'll hit it too.
Intelligence came about because at every stage in the development of primates, the ones who are just that little bit smarter than everyone else will always have the advantage. Over millions of years, it all adds up. Along with this comes morality (since good deeds are often rewarded), an appreciation of beauty (since it helps if what's pleasing to the eye is usually not diseased, poisonous or dirty) and emotions (to motivate us to do what's helpful to us and others).
Going back to the origin of life, abiogenesis as it was called could have occurred by a number of different chemical processes. So far scientists have used electricity (lightning) and a replica of the ancient atmosphere to create amino acids, which are pretty close. With a whole world full of chemicals being blown and washed into each other and billions of years to work, there was ample time and material for the components of the first replicating organism to slowly accumulate. The huge odds against this often given by folks like Hoyle generally assume that they all had to come together at once, which they didn't. Once one little bit of DNA was off and running, evolution and exponential growth took over.
Before we tackle the whole universe at once, let's consider Earth. Someone might claim that God put Earth exactly where it needed to be relative to the Sun so that liquid water and therefore life could form. We now know, however, that there are a lot more planets out there, and probably huge numbers of undiscovered ones. It's not that Earth was placed where liquid water could form. Rather, liquid water only forms on planets of the right temperature and Earth happened to fit the bill. Lots more planets might. This is called the anthropic principle: places aren't made for humans, humans just have a chance of turning up in hospitable places. Even on Earth there are many places we can't survive, like inside volcanoes and kilometres under the sea. So, we didn't emerge from there. Big surprise.
The largest design claim has to do with the fundamental constants of the universe. Six major ones are usually mentioned: those pertaining to gravity, electromagnetism, spatial dimensions and other less famous concepts. As is repeated endlessly, the slightest difference in any of them might result in matter being unable to form or stay together. This is the "fine-tuned universe" argument.
The problem is that even if this is true, there could still be other values of the constants which support matter. Perhaps instead of changing one or two slightly, you need to shift four of them by a huge amount. Considering that some of the constants could even be negative, you've got an infinite six-dimensional sample space in which to test hypothetical universes. We may never know whether our values are the only valid ones. Or, we may stumble upon another valid combination and that'll be the end of this argument.
Besides, the anthropic principle applies again if you consider the theory of a multiverse. If there are multiple (perhaps infinite) universes each with its own set of constants, of course we're going to turn up in the universe with a friendly combination. Other life forms may be thriving in universes where we wouldn't last for a second, and understanding how would require us to re-learn physics from scratch.
Contesting the argument from design is hard work, because to be most effective you need to know the going theories for whatever phenomenon is in question. I've tackled the most common ones, but be prepared for just about anything useful or pretty to be presented as direct evidence for gods. Then you need only find out where it really came from.