The most recent evidence I've seen for cooking is: http://www.nature.com/news/million-year-old-ash-hints-at-origins-of-cooking-1.10372
In summary: there is some contentious evidence of controlled fire with bone fragments in Wonderwerk Cave in the Northern Cape province in South Africa, dated to about 1mya. There is much stronger evidence of cooking dating to 400kya, which is still some 200k years before the emergence of modern humans.
As for talking (as opposed to simple vocalisations), this is even more contentious. The Wikipedia article (https://en.wikipedia.org/wiki/Origin_of_language) is a good summary, positing the first controlled vocalisations were from Homo heidelbergensis (600-200kya for certain, but perhaps as old as 1-1.3mya).
Compared to heidelbergensis, Neanderthals (300kya) had a much enlarged hypoglossal nerve (for control of the tongue) and throat bone (hyoid) similar to ours indicating language had started by this time.
With regard to meat going off, I'll have to disagree with you. There are numerous species that eat rotting/rotten meat such as lions, hyenas and vultures (yea!) without harm. Indeed humans do too - here's a link to Reddit on the topic: http://www.reddit.com/r/askscience/comments/19ztos/why_is_it_that_animals_can_eat_rotten_meat_and/c8syno1
I actually saw the documentary seen by jetpacksforall - it made my stomach churn just looking at it, but only the ethnographer and crew seemed concerned in any way. I suspect that those children that can't fight of the bacteria don't make it to reproducing age :(