I won't link to any studies but regarding [2] (gut microbiome] does affect it ever so slightly. I'm just stating things from memory now, but I remember reading that our gut bacteria now is different from 50 years ago in such a way that a person eating (for example) 2000 calories then, would now have to eat 2200. Made up numbers, but the effect was between 5-20%.

As for your last question (food composition and satiety), tangentially related, in the literature regarding this it seems as if keto has a lot of support for weight loss. Not because of the way it affects your metabolism or gut bacteria, but because it does satiate people more adequately than other diets it was tested against (regular western, Scandinavian and paleo).