Tsk tsk tsk, careful not to put too much citrus in there too, it upsets the pH

Though, frankly, I think you'd need to be running some pretty wholesale orange-squeezing operation for that to make very much difference!
I would chuck barbie ash in, can't see why not.
My biggest composting sin is to shove loads too many grass clippings in, which then form a solid layer that nothing can get through, and then decompose, anaerobically and stinkily until I realise and give it a good stir. If you get it about right, you often don't actually need to mix the heap at all, but I think that's probably some kind of composting nirvana state: I certainly haven't reached it yet...