... part two
Some pockets of knowledge would survive. Some pockets of people with a strong genetic tendency toward one or the other of the talents would survive. I'd suspect the people of Cosmo Canyon were originally able to communicate with beasts - resulting in the evolution of the species Nanaki winds up being the sole visible representative of in the game. The family Aerith was born into was probably a family of healers and empaths - it's a talent which would survive just about anywhere, because people find it useful - and one which probably descended from the last group to leave the Ancient City (with a mission to remain near the crater, and make certain the Crisis remained sealed away). I've no doubt various families and bloodlines across Gaia would have various types of family lore passed down from culturally Cetra ancestors. Not all of them (it's clear within the game both Barrett and Elmyra are from families which had no tradition of "returning to the Planet" when you died; likewise it's clear in DoC that Shalua and Shelke Rui were from a family which did have this tradition) and not all the knowledge would be evenly distributed.
I agree with you the Planet would have paid very little attention to the amount of death it caused in its efforts to deal with Jenova. I strongly suspect Chaos may have come out of his original hiding place during this time (which would have *really* worried the Cetra, being one of the definite signs that The End Of The World Is Really Nigh) which might account for the way Chaos wound up sealed in the mako crystal in the cave up behind the Nibel Mountains. It's said during the game itself that the reason there's so much ice and snow (on an otherwise tropical, or at least temperate planet) at the northern continent is because the Planet still isn't able to spare any of the lifestream to provide plant cover there. The high monster population in this and other low-fertility regions (the Corel desert, the Midgar barrens etc) is probably due to the Planet doing its best to harvest as much of the Lifestream energy in the area as possible.