"Likewise, many cosmologists have articulated various forms of what is known as the “anthropic principle” — that is, the observation that the basic laws of the universe seem to be “fine-tuned” in such a way as to be favorable to life, including human life."Simple answers to this: (a) we have far too few examples of life (on a galactic scale) to gauge the actual "Goldilock" range for life suitability, and (b) we have a documented tendency to assume agency even in its manifest absence, which renders all such anthropomorphic impressions highly suspect.
"In that case, we are still left without ultimate explanations as to why that universe exists or has the characteristics it does."
Begs the question of whether "why" even matters at such a scale. Like the "then what created god?" question, the chain must either stop somewhere or recede infinitely to a "bad question" asymptote.
"For a complete evolutionary account of a phenomenon, it is not enough to construct a story about how the trait might have evolved in response to a given selection pressure; rather, one must provide some sort of evidence that it really did so evolve."
Apply that same criteria to all other non-evolutionary explanations, then come back with their relative measures of predictive value. Who wins that tournament of efficacy?
"For comparison, we know a quite a lot about the physiology of digestion, and we are able to describe in great detail the physiological differences between the digestive system of a person who is starving and that of a person who has just eaten a satisfying and nutritionally balanced meal. But this knowledge contributes little to solving world hunger."
The discovery and implementation of a system that makes hunger more objective, for example, would help address work hunger by freeing up overeaten food for those in greater need. Unimpressed.
"Harris seems to think that free will is an illusion but also that our decisions are really driven by thoughts that arise unbidden in our brains. He does not explain the origin of these thoughts nor how their origin relates to moral choices."
What about the receipt of controlling, "unexplained" "unbidden thoughts" contracts a disbelief in free will? The claim that Harris leaves them "unexplained" or unrelated to moral choices speaks more to the author's ignorance of Harris's work than anything else.
"This view [emphasizing the impact of genes and circumstance on the frequency of "moral behavior"] undermines the possibility of happiness and moral behavior for those who are dealt a bad hand, and so does more to degrade than uplift at the individual level."
Try telling that to had their "moral" capacity demonstrably inhibited by damage to their frontal lobes.
Any hope of addressing such organic damage to impulse control lies in the advancement of neuroscience, which might provide an actual fix.
The alternative equates to expecting a computer user to search online for their own answer as to why their Internet connection is down.
"Continued insistence on the universal competence of science will serve only to undermine the credibility of science as a whole. The ultimate outcome will be an increase of radical skepticism that questions the ability of science to address even the questions legitimately within its sphere of competence."
A straw-man, then begging the question. Given how much we know of the foibles of human cognition, perception, and recollection, the responsibility for taking something out of the sphere of science lies with those who would attempt the removal. Best of luck doing so without hard data, i.e. science, though.
tl;dr: a biologist reaches far outside her area of experience (and into, e.g., neuroscience) in order to try and fault the scientists actually in those fields for finding scientific answers to once-philosophical questions in their own fields. That, and the author's ultimate position boils down to an argument from consequence.