"Péter is hearing students outside."
Translation:Péter kint diákokat hall.
...does this mean that Peter is outside, or the students? Does the placement of "kint" matter?
Péter is outside. If the students were outside, you would use kintről (lit. "from outside")
I beg to disagree. The students are most probably outside but Péter can be either inside or outside. It is ambiguous, at least to me. But if we say "kintről", then yes, Péter is definitely inside. And we can say "odakint" in which case he is most probably also outside.
"Péter hallotta kint a diákokat", "Péter hallja kint a szirénát", etc. Péter could very well be sitting in his room.
I think that this sounds off in English. "Hear", like many verbs of perception (see, taste, smell etc.), have a different meaning when used in the continuous tense. It should be Peter HEARS or CAN HEAR... not *is hearing.