Translation:We run through the building, jump out the window and swim across the river.
"Across", to my understanding, is reserved for more flat, unenclosed spaces. Particularly where I don't have a roof over me. "Across the house" sounds to me like I'm on the roof. (Which would also be a good translation for the Hungarian sentence, were it not for the general lack of windows there to jump out of.)
RyagonIV As regards buildings, I agree, but you can say, "I ran across the room", "I ran across the carpet/floor/paving stones", etc. I think it's not about being enclosed or not; it's the idea of movement across a plane- no, I don't mean a plain or an aeroplane :)- a surface of something. Through suggests you are within it- it has a more 3D idea about it, and has more of the idea of obstacles in the way. "I walked slowly through the room between the old boxes and dusty furniture."
Basically, whenever there's a medium through which you're going or which you're using on your way, you use the -n suffix. Especially when using át-:
- átmegyek az utcán - I go across the street
- elmegyek az utcán - I go along the street
- felmegyek a lépcsőn - I go up the stairs
- lejön a kéményen - he comes down the chimney
As far as I'm aware it would be "átmegy a tengeren", or better "a vízen", no matter if it were surfacing or .. is it called "diving"?
You can make a difference by using more appropriate verbs.
- átúszik a tengeren - swims across the sea
- átmerül a tengeren - dives through the sea
Or just say "a víz alatt".
The problem is the way Hungarians and English see spaces.
Átfutunk az épületen - the "through" is the át in átfutunk (more literally across but we don't say that so much in English). Where do you run through? the building. Now I would have thought "in" the building - Átfutunk az épületben - but it is big enough to be seen as a unenclosed space - like a square - or a bus - and uses the superessive instead.
kiugrunk az ablakon - clue to this is when you look (in English) through a window, in Hungarian you use the superessive. Just memorize it :-( But the motion is in the KIugrunk - OUT jump.
átúszunk a folyón - the át is across. But when you are swimming you are on top of the water so the superessive is clear.
An excellent question and it builds on the earlier ones. The preverb "at" can obviously mean through or across or over and it all depends on the context. The first time it came up as through was strange for me but, like many English words, it has its variations and this is helping.