How did life originate? How did life with hundreds of proteins originate just by chemistry without intelligent design?
Random chance, around volcano of heat vents. Possibly through comets delivering things as well.
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 letters—just 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?
Natural selection. RNA more than likely came first as it is able to carry very simple things and could be used to pass on traits. DNA is less fragile than RNA however and eventually DNA became the gold standard.
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?
You'd be surprised how long four billion years is.
Why is natural selection taught as ‘evolution’ as if it explains the origin of the diversity of life?
Natural selection means species with the best traits for their environment will get to reproduce to pass on their traits. Because not all traits are favorable to all conditions, there is diversity.
How did new biochemical pathways, which involve multiple enzymes working together in sequence, originate?
Natural selection is my short answer here. To be fair, I haven't read that deeply into it.
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?
This is a fallacy. Just because something "looks" as if it was designed means nothing. Because of this, logical doesn't even begin to factor in since the alternative to evolution isn't logical.
How did multi-cellular life originate?
The same way protocells originate. Natural selection is about getting the best traits for the environment. Like DNA, mulch-celluarity proved beneficial to prokarayotic (sic) and eukayrotic (sic) cells.
How did sex originate?
Why are the (expected) countless millions of transitional fossils missing?
Because the world isn't perfect.
How do ‘living fossils’ remain unchanged over supposed hundreds of millions of years?
Because eventually, a species achieves genetics that is perfectly suited to its environment.
How did blind chemistry create mind/intelligence, meaning, altruism and morality?
Emergent properties of all these things.
Why is evolutionary ‘just-so’ story-telling tolerated?
Huh?
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?
Umm...what?
Why is evolution, a theory about history, taught as if it is the same as this operational science?
The same way the Theory of Gravity is taught as why big, heavy things are attractive.
Why is a fundamentally religious idea, a dogmatic belief system that fails to explain the evidence, taught in science classes? If “you can’t teach religion in science classes”, why is evolution taught?
Well, because biology is built around evolution. Evolution isn't a religious idea, it is a scientific idea. While there are disagreements to how
exactly life started, there have been experiments done including experiments that determined that life probably sprung around volcanoes or that comets brought amino acids.
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Also, scientific theory is extremely different from normal theory. If you believe in micro evolution, you have to accept macro evolution occurring over long periods of time.