Is the answer to this question expected to be "you are my sister" or "our relationship is good"?
The former. 'How is our relationship?' would be हमारा रिश्ता कैसा है?
Is this just family, or could it also be asking friendship or romantic relationship?
This would actually mostly be for friendships/romantic relationships (romanships?). Most cousins are just called bhai or behen (if that). And it's kind of awkward to ask a relative how you relate to them.
Another one: How are we related?
रिशते में हम तुमरे बाप लगते हैं।