I'm going to take a crack at these questions. Note that I'm not a professional biologist, although I do have university training in it, and do this mostly to inform myself and see where the conversation leads.
How did life originate? How did life with hundreds of proteins originate just by chemistry without intelligent design?
The Miller-Urey experiment, performed in 1952, established that complex organic compounds necessary for life can be created from pre-existing, non-organic compounds under conditions similar to primordial earth. Sidney Fox and Alexander Operin later showed that such compounds can aggregate into 'protobionts' that are may be precursors to prokaryotic life. This has never actually been proven beyond reasonable doubt, but it's certainly a possibility.
As an aside, evolution itself deals solely with intergenerational genetic variance and questions of the ultimate origin of life are largely moot as they neither prove nor disprove the theory in any way.
How did the DNA code originate? The code is a sophisticated language system with letters and words where the meaning of the words is unrelated to the chemical properties of the lettersjust as the information on this page is not a product of the chemical properties of the ink (or pixels on a screen). What other coding system has existed without intelligent design?
Again, I'm not a microbiologist, so take all this with a grain of utter disregard. In the 'RNA World Hypothesis' it is believed that the most rudimentary lifeforms functioned solely on RNA, which is both able to convey genetic information like DNA does, but also perform the role of catalyzing chemical reactions. RNA then evolved into DNA (it's been shown to be possible, in lab research) and proteins because both were better suited at their respective niches - genetic transmission and biochemical reactions respectively.
As for the second question, as I understand coding to be transcription of information from one form to another, I guess that basic chemistry of the elements could largely be considered a coding system. The subatomic composition of the elements dictates their interactions with other molecules and shapes the physical properties of the universe.
Oh, also String Theory, because the varying vibrational frequencies of the strings leads to the development of the forces and particles of space and time.
How could such errors (mutations) create 3 billion letters of DNA information to change a microbe into a microbiologist? How can scrambling existing DNA information create a new biochemical pathway or nano-machines?
I don't think I'm getting this question. Is it really just asking how the process of going from DNA to living biological entity works?
Why is natural selection taught as evolution as if it explains the origin of the diversity of life?
Natural Selection is a fundamental component of the evolutionary theory. Environmental selection of favourable phenotypes leads to the expansion of the population in question and therefore the propagation of it's genotype. Again, either I don't understand the thrust of the question, or it just doesn't make much sense in the first place.
Maybe they're indicating that there's some confusion between Natural Selection being
part of Evolution, as opposed to the entirety of it?
How did new biochemical pathways, which involve multiple enzymes working together in sequence, originate?
This is pretty far from my comfort zone, but after some research I feel like I have a reasonable guess. New pathways open up due to random genetic mutation and the quickly obtain the required enzyme because, due to something called the 'Screening Hypothesis,' there is a large diversity of inactive chemicals in an organism. These redundant chemicals are produced as side-effects of other, beneficial, processes. The great variety in available chemicals ensures that new pathways will have a fitting enzyme readily available when they evolve.
Living things look like they were designed, so how do evolutionists know that they were not designed? Why should science be restricted to naturalistic causes rather than logical causes?
Trying to prove a negative isn't exactly the most logical game in town.
The second question here actually threw me for a moment. Ultimately, I believe that the scientific method is fundamentally tied into naturalistic explanations because it requires measurable, empirical proof, and a testable hypothesis. My real concern was remedying the physical necessities of science with the more abstract reasoning present in mathematics.
How did multi-cellular life originate?
There are several credible theories for this process, but the one that is most accepted by the community (and makes the most sense to me) is the Colonial Theory. This theory states that a collection of single-celled organisms either separated and later reformed or never fully separated after cell division in the first place, creating a mock-multicellular creature. After the single celled organisms have coagulated, they then begin to differentiate into specialized roles, forming the basics of a multicellular organism. The reason this theory has such credence is that the process has actually been observed in taking place in slime molds.
How did sex originate?
This seems to be actually one of the trickier questions, as there is doesn't appear to be one commonly held theory. There are, however, many available explanations that make perfect sense to me.
One of these theories holds that simple organisms, when their DNA was damaged, replicated the structure of similar, nearby, organism in order to repair itself. Another that sex evolved out of a form of cannibalism in which one organism enveloped another but absorbed, rather than broke down, it's DNA.
There are more but I don't want to go into huge detail here. The take-home message here is not that there's no idea how it evolved, just that nobody's exactly sure which process is correct.
Why are the (expected) countless millions of transitional fossils missing?
They're not. There have been multiple transition, or 'missing link,' fossils found to date. In fact, I was downright amazed at how many have been discovered. I knew a few off hand, but when I ran a quick search I was shocked at the results.
Here's a list.
The article itself cautions that many of the fossils are not true 'transitional' specimens, but nevertheless this indicates a great deal of genetic drift over the millenia. Also, the fossil record is incredibly incomplete because of the sheer magnitude of the task.
How do living fossils remain unchanged over supposed hundreds of millions of years?
The first issue here is that majority of 'living fossils' actually have changed, albeit only slightly, over the time frame. Evolution doesn't always have to proceed in leaps and bounds; in fact, it's almost always the opposite.
This is really a non-issue for me. If a species fits into an environmental just right any mutations will probably be non-competitive with the 'original' form and just die out. I don't really see how this is a refutation of evolution at all.
How did blind chemistry create mind/intelligence, meaning, altruism and morality?
Intelligence and reasoning are a major evolutionary advantage, our own existence and dominance is proof enough of this. Because it is such a powerful advantage, natural selection pretty much ensures ever increasing cognitive ability over successive generations. Self-awareness was really just another step along the path. Meaning, altruism, and morality are all effective adaptations for a species to develop. They lead to a cooperative social structure, which history shows to be much more effective in terms of species propagation.
Why is evolutionary just-so story-telling tolerated?
Because the alternative is much more ridiculous.
Where are the scientific breakthroughs due to evolution? Why do schools and universities teach evolution so dogmatically, stealing time from experimental biology that so benefits humankind?
Evolution is the bedrock of modern biology. I don't think this question needs much answering, it's kind of absurd.
Why is evolution, a theory about history, taught as if it is the same as this operational science?
Evolution is confirmed by operational science. Again, I don't know where they came up with this one.
Why is a fundamentally religious idea, a dogmatic belief system that fails to explain the evidence, taught in science classes? If you cant teach religion in science classes, why is evolution taught?
This is really the same as the last one. Evolution is studied through, and confirmed by, the scientific method. End of story.