Research on chimpanzees (the only other adept throwers in the animal kingdom) has shown that communication capability is tightly correlated with throwing ability. Primatologists also found that throwing ability was tied to a well developed area of the left hemisphere called Broca's area. This area of the brain is responsible for speech in humans. Therefore, some have suggested that accurate throwing may have been a form of communicative self-expression (i.e., I don't like you and I'm going to let you know about it by pelting you with rocks). I'm not so sure myself. I'd have to do some more research. And in terms of the difference between men and women - that would seem to support a hypothesis related to hunting. However, it is important to note that hunting with long-distance projectiles (e.g., spears) is a modern human development; no other Homo species I know of developed that technology or ability.
It most certainly could be. The reason I was slightly reserved with my analysis is because there seems to be competing hypotheses in the literature and I have only read the primatology literature on chimpanzee throwing. However, I have not read the paleoanthropological literature which may support the hunting hypothesis. Maybe EvoAnth can help!