So when does the live action show take place? I thought it took place a few years after the first movie, but that wouldn't make sense if the planet blows up at the end of the second movie.
The TV series took place in the year 3085. The original movie was set in 3978.
So the show takes place fore the first movie, the humans talk, and then become dumb rather quickly and stop talking for the first movie?
Well, yes, realistically, 893 years is "rather quickly" for an evolutionary change to occur; but this is the same universe that postulated, in the fourth movie, that the chimps, gorillas, and orangutans we know somehow mutated into their more humanoid forms within the 20 years since the third movie and had universally acquired the power of speech by the fifth movie, some 30 years later.
The fifth movie has a frame sequence showing verbal humans and apes coexisting in the year 2670. This puts the TV series more than twice as close to that era as it is to the era of the original film. If one accepts the conceits of the films' universe, it fits in rather logically; the harmonious ape/human coexistence seen in the fifth film's frame has broken down by the time of the series 415 years later, and humanity's lot continues to erode until you get to the degenerated state of affairs in the original film, 893 years further along.