Only if you're speaking colloquially. We get at least one thing in our own language wrong in almost every sentence we speak and there's no room for that in German.
He is the subject whereas him would be the object. If you rephrase the sentences slightly then you can easily hear which case it should be if you're used to the language. "Who did this?" "He did this"
We can get away with it in English of its SVO (subject verb object) sentence structure meaning we can pretty much use either the subject or object version of the word and as long as it's in the intended place in the sentence, it shouldn't break comprehension. German word order is very fluid though, so unfortunately the correct case muat be used in order to be understood.
Rufus This is interesting, as it only just about qualifies as a phrase, courtesy of the hyphen. But I have not seen two parts of a question written in this way. My preference would be 'Who? Him!' or maybe 'WHO, HIM?!' to use text emphasis. This 'controversial' pronoun works simply to assist speech. Hence its widespread, reasonable adoption,- language keeps evolving. However, if a sentence needs a verb, and a phrase needs two words (and meaning), is this simply an interrogative lone ranger, answered with a pronoun? The word Economical comes to mind. This light relief is based on a real interest in the grammar. I studied Auden, Camus, Zola and Shakespeare, etc, instead, as part of an experiment encouraging a deeper existential connection through the Arts.
Most english speakers would expect to hear "him" in a situation like this because, while the male being refered to is the "subject of discussion", he is not necessarily the "subject of the sentence [fragment]".
Grammatically, he is more likely to be the object of the sentence, which is fragmented here, but a way to help understand would be to flesh out these phrases:
"Who [are you referring to]?" "[I am referring to] him!"
"Who [are you in love with]? - [do not tell me that it is] him! [my brother!]"
It's not clear if there are supposed to be two speakers or one person is answering their own question as a way of seeking confirmation or clarification. Either way, in English you would most likely want to use "him" not "he".
You can use "he" (as subject) to imply something like this, "Who [is your doctor]? He [is my doctor]!" But that is a lot of specific information to leave unsaid or try to imply. So usually, in English, when someone just says, "Who?" They are likely implying, "Who are YOU referring to?" in response to something you have just said.
Who (was it)? (It was) him! Who (did it)? He (did it)! Both are grammatically correct, depending on which verb is implied. However, I would always use "Him!" and never "He!" as a full sentence, because "He!" just sounds wrong to me.
Another example is "Who (are you talking about)?" "(I am talking about) him!"
We just do not say this in everyday life. Who? Is a strong word. He! is not strong enough to fit this short question, so we use, "Who? Him!" Purists will tell you about the correct grammatical use of he vs him but, just as in French, some combinations just sound wrong. This is one. The 'm' gives closure to the phrase. 'He' sounds like you are mid sentence. The written grammar is more correctly He but for the reason above it does not sound or read well as a standalone. With apologies to any grammar 'police' but languages evolve and this is not as truly awful as 'this is me bike' (learners: 'my' here).