They may well have had fights with each other over anything from personal feuds to territorial or resource disputes.
They did not live "in harmony with Nature" in the sort of rose-tinted sense we often hear these days. I think that's really a rather patronising view of them.
Hunter-gatherer societies, of which a few still exist in remote areas, were likely only ever to have taken what they needed; but for purely practical reasons. They would know picking too many wild fruits at once is wasteful because fruit spoils very rapidly. They would not have killed more wild animals than necessary because such hunting is difficult, arduous and dangerous; and meat rapidly decays even in cool weather.
The supposed "harmony" with Nature is that their populations and predation rate were insufficient to cause much damage. They had to eat, they needed furs and bones; but they had to work hard and often dangerously to ensure this. They could not be squeamish or romantic about the fauna and flora.
The more settled people with some form of agriculture tended to be quite destructive, using slash-and-burn land clearances. If this had limited overall effect millennia ago that is only because there were far fewer people about; but mankind has been deforesting much of Europe and many other regions since the Bronze Age if not earlier. All that's happened is that we have become much more efficient and rapid at it.
This is not to say the ancients had no respect for Nature. I expect they did, as they often worked it into their own religions and myths; but it is hard to think they had the sort of "hippy-dippy" attitudes very comfy for us to assume they had from the safety of our comfy 21C homes.
Nature can give but also take away; can be beneficent and bountiful but also harsh and dangerous; so these people would have lived as best they could with it. They had to, to survive.
