I speak Russian at a native level, but that's an archaic pre-revolution orthography that I'm not 100% sure about. But I'm 99% sure that most of those transliterations are correct. Except Gorky. In Ukrainian Г makes a rough H sound, while in Russian it's G, as in "good".
And a bonus fun fact for you, горький (gorky) means "bitter".
They don't, actually. Most of AI stuff is processed on device, few go to their private infrastructure, and only certain Siri requests go to ChatGPT, if you give explicit permission.