Salam Arlana, Some people say both, and some other say just one of them. Usually when people want to seem very friendly or don't have much to say, use both of 'chetori' and 'khubi'. Have a nice day

Hahaha... You're right, they're rhetorical questions and sometimes if someone responded your "Chetory?" question by a simple "Khoobam, mamnoon!", and then you ask the "Khoobi?" question in a charming and cheerful way, not only it's ok, but it's kind of more friendly especially when talking to a kid. You know some kids are so cute and lovely when they speak, that you don't wanna stop talking to them!!!!! hahaha... my niece is one of them!!! I think in English they say: -Hey, how're you doing? you're fine? -fine! thanks! or maybe: -Hey, how's it going with you? is everything allright? -yeah, thanks bud.

It's not an obligation saying both of them but you can do it!(but normally people don't say two greeting expressions which would have the same response) it's like in English, you may say: how are you?are you ok? (chetori?,khoobi?)but when some one is answering to the first one ,nobody ask the second question! because that would be automatically ridiculous ! hope it is useful to get your answer :)

nobody here doesn't care how you say them ,together or separated best regards

Chetor = how, Chetori? = How are you? Khoob = good, fine, Khoobi? = Are you fine? I just remember that the ending -i shows the 2nd person singular. Btw, if not mistaken, bacheha = bachcheha = children / kids.