To clarify why: 'nedenfor' means 'down past' in the sense of below or under, not past. You are literally talking about a lower level than where you or something else is, not going past something. Below is the word I used in my translation, because I have never heard of the construction 'down past' before.
It does not seem to be "under" nor "below" here, but "down past the restaurant" or "down beyond the restaurant" Perhaps this is an idiom? "nedenfor" does mean below when talking about a page of a book or on screen as in "see below" with the meaning of "further down the page"... or "further along in the news article". http://www.nob-ordbok.uio.no/perl/ordbok.cgi?OPP=+nedenfor
Imagine you are on a hill, and down the hill is the restaurant, but your car is past the restaurant, if you follow the road, in the car park. You would say your car was down past, further down than or beyond the restaurant (although beyond can imply further away in a straight line). Think of it as "down (the hill and) past" hope this helps.
Down past makes sense to me. Restaurant is uphill so you go down (and) past it if you are also at the top of the hill. It might be a British thing lol. "Under" and "beneath" the restaurant would denote that whomever was in the cellar, buried in the foundations, or such like. Beyond, past etc... Although subjective, generally mean a point set further away than another point. Beyond may be becoming somewhat dated now, I imagine, in modern parlance giving way to 'past' etc
I'd say that "behind" is quite different. When saying "down past" it's referring to something beyond (but slightly below) the restaurant for example. This means that the object is still located on the same street. Using the word "behind" alters this. It suggests that the object is behind the restaurant, so literally behind it at the back of the restaurant, and not by the street. At least this is how I understand it.
Under the restaurant would mean literally under it. So like a floor below etc. Whereas this sentence refers to something that is on the same street as the restaurant but slightly below it since it's on a slope. (it's lower down on the slope than the restaurant and not directly below it.). I hope this made some kind of sense :)
You keep walking on the street, it's not everything in same level but more like a hill? One side higher than the other side. And u begin from the upper side. You ask where is the apartment and I tell you, u keep walking down (since you were on the upper side), you walk past the restaurant then you shall see it. XD I think thats the meaning. Not under the restaurant, not behind the restaurant.