You can definitely sit "in" chairs in English as much as you can sit "on" them, so "in tall chairs" should be acceptable .
In general terms a 'tall chair' would be regarded as a stool, and these are students so one would assume they are in a class. I would think 'sitting on' is correct here.
Both should be accepted. "In" is the usual idiom in English, and "on" is the direct translation of the Hungarian, perfectly understandable, and in certain circumstances might actually be correct.
You can only really sit IN a chair that is soft or has arms - but yes, both should be accepted.
So I can't say on THE tall chairs? Is there really a difference here?
Yes. "The tall chairs" (a magas székek) would refer to a certain group of chairs. "Tall chairs" (magas székek) just states that the chairs they're sitting on are tall.
You can't say "the high chairs" because there's no "the" in thr Hungarian sentence. When there's a "the" in English, there will almost always be one in Hungarian too.
I can't hear the s in magas either. I think it blends into the initial sz of székeken in a way that a native speaker might be able to tell the s is there but is tough for a learner.
You also cannot say "high chairs" because that means a tall chair for a small child to sit in with a tray for food and a bar to stop them falling out.
In the audio, I don't hear the "sh" sound in "magas". Is there a reason for that?
Because in English "tall" and "high" do not mean the same thing. "Tall" is of greater than average height while "high" is a long way above the ground. A chair would be "high" if it was hanging on a hook from the ceiling. Further the term "high chair" has a special meaning as a chair with long legs and a tray for children.