Translation:The sleepy student falls under the bench, on which I sit.
I'm not sure what is actually happening in this sentence and I wouldn't be so sure that the speaker is actually sitting on the bench.
Yes, this is interesting. Hungarian schools have, or used to have, a combined desk-bench piece of furniture, in one piece, called an "iskolapad" or referred to simply as "pad". You can search "iskolapad" on the internet for examples. Students would sit "in" the "pad": "a padban". Maybe sometimes "a padnál". It is indeed unsure whether the speaker is sitting "in" or "at" such a "pad".
Nel is by and re is on so naturally you translate nel as on and mark me incorrect. But if I’d translated nel as on you would have marked me incorrect as well. How am I going to gain any confidence in Hungarian if you keep changing the rules?