Hi Kooyeen.
Reported speech: you report information, and particles like "what, who, how, etc." don't change. Examples:
I want to know who that guy is.
I found out who that guy is.
This doesn't seem like reported speech to me -- I'm not sure what you would call the role of "who that guy is" in the sentence -- but yes, the sentences are correct.
But... you wouldn't say this:
He is who married my sister.
You say "He is the one who married my sister", don't you? Yes, that's right.
If I "we have to find who's responsible," I would think it was somewhat ambiguous and should be re-worded. It's certainly something people might say, though -- most people don't spend one-zillionth the amount of time thinking about language as we do here, and even pedants like us are not as careful (or obsessive) in conversation as we might be in writing.
So, here's why I said it's ambiguous -- "We have to find out who's responsible" means one thing, (we have to figure out who is responsible) and "we have to find the one who's responsible" (or "we have to find whoever's responsible") means something else (we have to find the actual person). "We have to find who's responsible" doesn't exactly say either one, but someone might say it intending either meaning -- or both at once. Usually, of course, you would want to find out who's responsible and then actually find that person, so most people would probably not spend too much time thinking about the difference.
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