1. It's not just that there were bigger predators, but there were more, larger fauna in general before the eruption of Toba. Lions are not too big for humans to overpower with the weapons we have. The fauna during the pleistocene were considerably more dangerous and harder to kill, but not impossible. My point was that there was more danger at that time. Since women are needed for reproduction and become really vulnerable during pregnancy and after childbirth, men became the hunters and protectors of groups. Women (and thus humans) survived better when the danger was faced by the men in order to keep the women and offspring safe.
2. These female animals are usually strong enough to defend against predators, fast enough to get away from them, or stealthy enough to avoid being spotted by them. With skill, humans can pull off the last one. Not to say they couldn't ever forage on their own, just that it would be dangerous in the pleistocene. We were better off armed to fight to protect our groups, and men were better for it because if one died, you could still have the same population in the future (and childbirth was fucking terror back then). The reason we became a group animal in the first place is because we could not survive in our environment doing our own thing like chimps do. It's not just that women develop a dependence on men, but that people develop a dependence on people.
3. I think the past 10k years of human evolution are significant, but not enough to overhaul the 200k before that. I speculate that the changes in human psychology have more to do with how we function within societies of the scale we started developing when we could farm, and less in the way of each gender's set of instincts involving mating. With the spread that the human population had 10k years ago, if there were any new evolutions to human psychology that reflected changes in the role of genders, I think they'd probably vary by race. I honestly never thought about it before, but it does seem possible based on what I've read.
I still do speculate about whether some people are more towards the beginning or the end of that 10k years in terms of traits. I've thought that maybe extroverted people are the people who are further along in the adaption to large societies, and that introverts are more adapted to pre-agricultural societies. I never thought about if it has anything to do with gender, but gender isn't my main focus. It's more something I end up picking up on the side as a result of the biological side of evopsych.