Translation:The tall trees are next to the hotel.
Do I understand correctly that the subject of this sentence is "a szálloda" and the object (in Accusative case) is "a fák"? If this is the case, why are the subject and object switched in English? Or rather: How can the subject (in Hungarian) be declined and be in accusative?
No, the subject is the trees: "a fák".
And nothing is in the accusative in this sentence.
"Next to the hotel" - "a szálloda mellett", is some kind of a locational case, I don't know the exact terminology. But it is not the accusative, for sure. Probably "locative".
Yeah, it could be. Hungarians do not really learn these things (including the various suffixes) as "cases". At least last time I checked it was not so. It is more like trying to fit a bunch of square pegs into one round hole. :) Matching the Hungarian system into a terminology that fits a whole big family of other languages.
As is traditional with grammar :) Even English grammar described using terms developed for Latin does not always work that well.
I don't think there is much difference. Beside would work in most of the same instances. But on the other hand I have next door neighbors or live next to my neighbor, but to say beside would not be used at all in the first case, and in the second it would imply closer living quarters.