Where can I find the list of iOS 8's 4000 APIs?

You can see the What's New in iOS 8 doc for a general overview of, er, what's new: https://developer.apple.com/library/prerelease/ios/releaseno...

More specifically, there's the iOS 7.1 to 8.0 API Diffs: https://developer.apple.com/library/prerelease/ios/releaseno.... Note that a huge number of the changes are just small changes to argument lists (there are a gazillion of these in Accelerate, filling the top chunk of the diff doc) and a number of other change come from the switch from (id) return types to (instancetype) in init: methods. Also, getter and setter methods have been replaced with properties in many classes, which doesn't break any existing code, but generates changes in the API diffs.