Will Apple still accept new iOS 8.4 apps? I have an app that's close to release. And of course, we didn't get in before iOS 9 came out.

Does apple still accept new applications that work in both iOS 8.4 and iOS 9.x or are we limited to only bug fixes, etc. for existing apps in iOS 8.4 (as we were with 7.x a few months ago), and only releasing new apps for iOS 9.x?

Is there a definitive web page for this information?
Yes. Apple checks your new app submission with the validator as described in https://developer.apple.com/library/ios/documentation/IDEs/Conceptual/AppDistributionGuide/UploadingYourApptoiTunesConnect/UploadingYourApptoiTunesConnect.html#//apple_ref/doc/uid/TP40012582-CH36-SW2

The iOS 9 features were allowed on Sep 11 2015 per https://developer.apple.com/news/ and you are allowed to use iOS 9 only SDK but you're not forced to use them exclusively. Any non-deprecated API are safe to use.