I have similar problems. I have an iPad Air 2 and I’ve updated it to iOS 9.0.2 recently. Mainly the lock screen and home screen won’t change orientation when I rotate the iPad. The only way I can rotate the screen is if I rotate the iPad then slide to another page (page 2 or search page). All my apps work well when I rotate the iPad, but not the home screen or lock screen. I also use the ‘speak screen’ feature sometimes, the words are supposed to be highlighted when being said but the words aren’t highlighted, instead the highlighting goes the wrong way across the screen (this must have something to do with the orientation), for example: if I turn on ‘speak screen’ the highlighter goes up the screen not over the words.
I’d appreciate any advice, thanks.