I got "Our airplane is flying over the sea." as a correct solution. But "over the sea" is "nad mořem", isn't it? So I think this solution is not correct. .
Possibly... I know overseas is across the sea, but that is an old word.
An then "My bonnie lies over the ocean", but that is both old and Scottish.
It appears that NAD can be translated as both "above" and "over." Both are included in the accepted translations for this sentence. UPDATE: PŘES, the preposition used in the sentence, also can mean both "over" and "above."
In my understanding "above" is indicating the location, while "přes" indicates the direction. Isn't that a big difference?
Yes, there is that difference. Here our flying airplane is moving across the sea from a point in the sky that is above/over the sea. I imagine that the creator of the sentence chose PŘES as the preposition to use in describing the plane's activity because it is the most appropriate. (Since I am not a Czech expert, I can't address that directly.)