'Social structure was simple and egalitarian."
Impossible to know. Extrapolating from modern hunter gatherer societies living nomadic lifestyles, it's hard to accumulate material goods so individual status is possible (gained by skills, strength, or knowledge,) but hereditary status is harder to accumulate (harder, not impossible - see other primates). Heierarchies therfore tend to be small and simple.
Likely; not proven.
"Groups needed all hands to ensure an adequate food supply,"
Yes. But
"with men responsible for hunting large animals and women, for gathering plants and small animals."
This bit's woolier. Again, extrapolation from modern hunter gatherers tends to support some sex-based specialisation. But it's not complete or universal, or necessarily based on size (in some communities women and children do fish and frogs; men do birds and mammmals - but the sizes of the prey species aren't that different). Often plant gathering is both men and women. And some archaeological finds are now providing suggestions that prehistoric women were also involved in large animal hunts. A lot of this will depend on habitat and types of prey available - historically humans had a wider diversity than modern hunter-gatherers, with more big game that lends itself to whole-ccmmunity hunting efforts.
Unproven, verging on dubious.
"The ubiquity of so-called Venus statuettes and the central position of female figures in Paleolithic caves indicates that hunter-gatherer societies roughly balanced gender power."
We all know archaeologists are fond of describing everything of unknown purpose as a 'ritual object'. Doesn't mean they were. Prehistoric venus statues may have been objects of worship. Or they could have been early PornHub. Who knows? Even if goddesses were worshiped, that doesn't necessarily translate to the status of living women. See the treatment of women in societies that venerate the Virgin Mary.
And the gene stuff is nonsense, as already described by PP.