Any cat person who's had cats for any real period of time knows why a cat kneads. In my family, we call it making biscuits.
For the other point, there are "experts" who would say that a cat brings its prey to its master in hopes that the master will eat it; it wants to feed us, not just have a safe place to munch down. There was a video done of house cats who went about their day with a camera attached to their collar (Cat Cam), and it showed how many small animals they went around killing and eating. It was an insane amount of killing, and most of the time, they didn't bring their prey home to eat it because they wanted a "safe place" to do so. I know with my three cats, it's "rare" when we actually see what they catch, either dead or alive, so can you imagine how many they actually do catch?