For a war-torn Earth to repair itself without people around to keep mucking it up?
Otterella,
There recently was a TV documentary series, Life after People, which speculated on this. It examined how long it would take for human cities and structures to deteriorate and for nature to overtake such cities.
It ran (or is still aired) on the History Channel. It doesn't examine or explore 'why' or 'how' humanity disappeared, just what happens once all people are gone.
It also speculated somewhat about the altered flora and fauna. This series might answer some of your questions, or at least give you some ideas.
Check out the link for more information: Life After People (History Channel Link).
As far as what exactly "repair itself" means, take it as you like. Mostly, how long would it take for a desolate wasteland to support human life again, if humanity was enclosed in a handful of self-sustaining population-controlled cities.
That's not really true. Again, it depends on destruction levels, but soil regenerates itself via new layers of OM and the natural processes that create soil in the first place. It wouldn't take long for soils to regenerate after farming ceased in an area where there were the right conditions for that soil to exist in the first place.Soils that were ruined by irresponsible agriculture will likely never be as productive as they were.