Not very likely - fire and tool use both predate* H. sapiens and H. Neanderthal,*, originating with H. Erectus if not earlier. Our ancestors had fire and tools before they were human.
Tool use dates back to at least H. Habilis, even earlier than H. Erectus. Hell, it most likely dates back to the common ancestor of chimps and humans.
Um… that would be our ancestors before chimps and humans diverged. Actually, scratched that - pretty much any omnivorous animal could be described as a “hunter-gatherer”.
Nope. At least, not our closest relatives.
Um… chimpanzees have been observed in the wild actively hunting, killing, and eating monkeys. In addition to eating insects.
“Stone age tools”, again, go back to before humans were human. Before the species could even be part of the genus Homo. There are not and never have been humans without tools.
We’d be handicapped by being considerably weaker than our closest ape cousins. But yeah, we might be able to survive for a time. I don’t we could do it long term, our young are too vulnerable, keeping ourselves fed would be difficult. We evolved as tool users. Not just H. sapiens but about 3 million or more years of evolution through at least a half dozen species, all of them tool users. “Uses tools” is as much a defining trait of H. sapiens as “uses language” and “is a biped”.
I don’t know the formal name, but “common ancestor prior to the split to chimps, gorillas, and humans”. Chimps use tools, even make tools by modifying branches to shapes better suited for things like termite-fishing.
Some foods are toxic if not cooking. Cooking obviously makes them a food source that would be otherwise unavailable.
Cooking can soften fibers and alter the chemistry of a food, allowing for easier digestion, resulting in greater net calories.