"Perfectly" is a stretch. No natural process has been shown to assemble amino acids into living organisms. (Of course, this is not evolution per se, so let's try not to de-rail.)
Aminos to monomers, monomers permeate lipid membrane bubbles, those monomers combine into chance assemblages of polymers, some of which are inevitably self-replicating, and from there evolution can take its course.
All the basic body plans found in nature today did not appear gradually, but suddenly, in the (pre)cambrian era, founding the diverse "lineages of almost all animals living today."
Define 'sudden'. If you're referring to the 'Cambrian explosion', it's worth pointing out that this 'explosion' took tens of million years, and is primarily typified by the appearance of
hard body-plans. Extant body-plans may well have evolved much earlier, but until they could readily fossilise, they wouldn't appear in the fossil record. Come the Cambrian explosion and your body plans are now fossilising - which would show a 'sudden' appearance in the fossil record.
Indeed, according to
this source, the Cambrian explosion is no more 'explosive' than any other point in the history of
Animalia - it's not that anything special happened with regard to how quickly new body plans were developing, but rather the explosion simply represents the evolution of hard body parts. As evidence accumulates, we see a bigger picture, and the 'explosion' turns out to be nothing of the sort.
Further, most of the organisms in the fossil record before this time either died out (no longer passing on genetic information) or persisted relatively similarly (bacteria, plankton, and algae).
Define "relatively similarly". Bacteria are one of the most diverse groups of organisms on the planet. Just because they're small and unicellular doesn't mean they haven't changed.
This is contrary to the Darwinian tree of life, and common ancestry from one living organism to many over time.
How in the world did you conclude that?
(So primates may have common ancestry with other primates, but the idea that primates and fish have common ancestry is not represented in the cambrian explosion.)
Not really: the ancestors of primates during the Cambrian explosion
were fishes.
Also, natural selection is problematic in that genetic mutation tends to cause problems rather than aid survival and adaptation. For that matter, I'd like to see actual examples of mutations increasing fitness, if anyone can provide links, as well as evidence that a change in genotype can provide a new phenotype rather than variations on existing phenotypes.
There are two examples I like the best: nylon-eating bacteria, and
Lenski's citrate-eating E. coli. Both show clear instances of the evolution of novel, hitherto non-existent traits.