"Who is watching him?"
The -i ending :)
It's definite conjugation, so there has to be a definite object -- "the man" or "him" or "that person" or something definite.
Even if it's not stated in the sentence, you can understand from the verb conjugation that there is a definite object in the meaning.
How do you know it is a person? Could this sentence also mean "who is watching it". As in a new movie is playing and you ask "Ki figyeli?".
Yeah, sure. It could also be an inanimate object or even multiple objects. The only thing we know through the use of the definite conjugation is that it's a certain object we've mentioned, So "him", "her", "it", or "them" (or even a formal "you") are good translations here.
"Watching a film" wouldn't work here too well, though. That usually uses the verb néz. Figyel is more "to pay attention" or "to watch out".
It doesn't accept "Ki nézi". I don't know why, It's correct according to a hungarian friend.
That is the correct answer, as it is a complete one, and much closer to the original sentence. The proposed one, which is now "Ki figyeli?" is a defective sentence, since it lacks the definite object. It is maybe implied, but we do not know that for sure. IMO, the defective solution is only making it harder for those who are willing to learn the language. In this exercise, they should focus on how the existence of a definite object influences the verb. And, guess what, we barely scratched the surface of the definite conjugation, and we have already come over a sentence where there no object is present, and the explanation is that it should be implied from the context. But, there is no context here. These are only standalone sentences. IMO, this is as improper language teaching methodics as it could be... Students shouldn't be exposed to such a confusing influence, especially not if they are only trying to acquore the Hungarian definite conjugation and are still struggling to understand the differences between the definite and indefinite ones.
So, there is no way of knowing if you are being asked "Who is watching him, or her, or it, or you?
If you're being asked "Ki figyeli?" by someone, you both should know what is being talked about. The child, for instance. Or the cookies in the oven. There usually has a dialogue happened before that states what this is about.
Out of context, like here, it can mean 'him', 'her', or 'it', or the plural 'they'. Hungarian doesn't make a difference of the genders anyway.
It won't be 'you', though, at least not the informal variants of te and ti, since those require the indefinite conjugation to be used: "Ki figyel téged?" - Who is watching you?
I think in those cases it's much more polite to spell out the object as "Önt ki figyeli?" and similar.
What about "Ki vigyázza rá"? Because I would interpret this as "who is watching him (a child)?"
I understand where you're coming from... in American English we would say "The babysitter is watching the children" (and I think in Brit. Eng. they say "minding the children"), so when I saw the English sentence "Who is watching him?" it's more natural for me to assume someone is asking a parent who is watching their child.