Will Apple still accept new iOS 8.4 apps?
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.