You're covering material that has been very well trodden and refuted a myriad of times.

The only novel claim is believing Flew's book title and then warping it into "most popular" instead of "most notorious". Flew was never the most popular atheist, not in any recent era, anyway. Bertrand Russell had him incredibly outranked until his death in the 70s, and Dawkins was immensely ahead once The Blind Watchmaker was published in 1986. And in the 80s, Madalyn O'Hair was more notorious by a long shot than Flew was. So, no, don't believe Flew's title. It's certainly not true now.

Regarding your five points, as I said, all have been discussed and refuted numerous times, but I'll give you a brief flavor of each.

(1) Your entire argument boils down to a linguistic trick: you think that by adding the word "supernatural" you get to avoid causality applying to God. But this is no more rigorous than saying "only universes can be created from nothing". If you actually wish to go into details, you find that while conservation of energy is incredibly well conserved at all normal space and length scales, it's not nearly so clear at the very largest or smallest scales. But we don't even need to go here: you have simply played a linguistic game and declared that because you used a different word, you're right. An opponent can very well object: no, you haven't done anything except give yourself permission to break rules. We get permission too, or you don't. Fair is fair.

(2) "Design" doesn't require a designer. All it requires is the right kind of process. We know this because we can create this kind of process and observe that novel solutions come out of it as if by magic (e.g. evolutionary algorithms or simulated annealing). When we copy the logic of how evolution works--boom! Optimized outputs that we didn't anticipate! It is inherent in the logic and causality of the situation; that we realized this by exploring it no more means that we were the designer than us noticing that 2+3 = 3+2 means that we have designed the symmetry of addition. It's just how things work. Of course, with all kinds of specific supposed challenges to evolutionary "design" (and examples of poor suitability to purpose) you can probably find an extensive discussion at talkorigins.org. But the protestations of Behe and Dembski to the contrary, it's just not true that design requires a designer and in fact we've proved it to ourselves.

(3) Life doesn't demand a supernatural life-giver because life doesn't demand a supernatural life-sustainer. One of the triumphs of the last couple hundred years has been finally to unlock the mysteries of life. We now know what it is, what it isn't, how metabolism works, how heredity works, and more and more. It's all just physics, it turns out. No vital essence, nothing. It's true that we don't know precisely how life arose, and it's true that it's not an extremely common outcome for molecules known to be present in the early solar system, but that's not too astonishing. We lack planetary-scale labs to thoroughly investigate the matter. The key, though, is that there is no demand for a life-giver. If there had been a life-giver, well, once given, life would continue; but if there was not one and it was just physical processes playing out, that would have worked too: once started, life perpetuates. It's also not the case that if abiogenesis can happen, that we should know how by now. Not remotely! There's been vanishingly little research, at scales billions of billions of billions of times smaller than the original (plus we have only a very sketchy idea of what was even present). We haven't tried everything and always come up empty-handed; compared to what there is to try, we've tried approximately nothing. (There is a LOT to try!)

(4) Moral law isn't a thing you can point to and say, "there it is, explain that!". All we have are our own feelings about how to treat each other. As it turns out, our moral intuitions make rather a good deal of sense in an evolutionary context of competing and cooperating tribes of a few dozen or few hundred individuals. Of course, we want there to be a universal objective moral law. Wouldn't that make things easier? But wanting something doesn't make it true. What we actually know that we have is something that is very comfortably explained without any reference to anything supernatural. (Indeed, it would be rather surprising if we didn't have it.) We then use our powers of generalization to universalize it, and with good reason, I'd argue. But not because it's a thing that is definitively there. Quite the opposite: it's pretty explicitly something we're doing ourselves.

(5) Free will has equally bad problems with both materialism and theism. A variety of atheist philosophers--Patricia Churchland for instance--think that mostly we've gotten confused about what our will actually is, and that because of this confusion we pose questions that are insensible, and then use our confusion about our insensible questions to draw unfounded conclusions. (Her arguments are more nuanced and insightful than this, but this is my rough characterization of it.) Indeed, you need to come to a very similar kind of conclusion if you're going to save free will from strong theological determinism: assuming you don't want a weak and limited God, you kind of have to redefine what you mean by free will. Without getting into any more details of philosophy, it's a big problem for ideas of free will if you either have anything all-knowing (i.e. you could not have done otherwise) or if you have a deterministic or random process (either God-willed or mechanical--either way it's not you choosing). So the problem of free will is that we've decided we have something that is incompatible with any idea of how it could work. Oops. Anyway, there are both theistic and atheistic ways to save the situation, so it's not the case that God is necessary. (See, for instance, the Stanford Encyclopedia of Philosophy on free will, plus related articles. Especially check out Compatibilism.)