But in science, the word "fact" can only ever mean the former, and never the latter, because even the most well-established observations and experimental results run the risk of being overturned. So your quarrel is not with this essayist, who is using the word "fact" in a sense roughly congruent to what scientists mean, but to the use of the word "fact" in scientific discourse at all. (Indeed, the essayist is beyond reproach on this score, as he quite carefully spelled out which definition he meant.)
Yes, but not really. My main comment is that quotes or no quotes in the context it is meaningless.
Facts are objective, not opinion. There facts that support evolution or other theories.
Let's look at the Fluid Mosaic theory of biological membranes. This was a theory developed and shown to be accurate, real, or even factual -- which would be the context of the use of fact in question. This is, though, that there were direct measurable physical observations that were factual in every sense of the word. To the extent that the theory was essentially fully encompassed in what was measurable and demonstrable, it is "fact" that membranes are lipid bilayers with proteins embedded in them. But to talk about the lipid mosaic model as "fact" would be strange.
Same for the determination of the genetic material -- was it protein or nucleic acid? It was demonstrable experimentally.
...there is a mountain of evidence that confirms the existence of evolution.
This sentence is nonsensical.
The existence of evolution. Where might this evolution be? Perhaps out in the yard? Shopping at the market?
"Confirms the existence of evolution" is meaningless gibberish.