Translation:The police officers are searching for him in the sea.
Even in English there is a difference in the geographic definition between a sea and an ocean: http://oceanservice.noaa.gov/facts/oceanorsea.html
It depends on how formally we are speaking. In everyday, casual conversation we can use sea and ocean interchangeably. But in a more formal/technical/academic discussion, we would not use the two terms as synonyms.
What i wanted to know was: can בים also be translated at "at sea" (meaning on a boat rather than in the water)? Are the police looking for a dead body or an escaped suspect?!
It gets worse. Israelis don't go to the beach, they go to the sea:
הולך לים - this is what you would commonly say, even if you don't go in the water.
הולך לחוף הים - This is logically correct, but is not what we mostly use
So the sentence above can mean that the cops are combing the beach looking for him. They don't have to be looking in the water.
These two words are pretty much interchangeable in English. Duo's other language courses are not so rigid. Will the Hebrew version be changed in this regard, or should we always try to be as literal as possible? Should I report things like this as errors, or should I just try to conform?
You cannot say "the Pacific Sea" or "the Mediterranean Ocean". So these words are not that interchangeable. Perhaps in Hebrew it's a bit more strict than in English. I don't think it should have accepted "ocean".
I think "ocean" should be accepted. In English, unless we're referring to a specific, named body of water (e.g. Mediterranean Sea), we do use "sea" and "ocean" interchangeably -- and, in America at least, we are much, much likelier to use "ocean." "Sea" sounds a bit quaint.
I agree that "sea" can sound either quaint or poetic. But we do use terms like "sea life" and "rough seas" (literally or figuratively) and the idiom "at sea" (confused). And if a ship goes down in the Atlantic, we still would say "lost at sea." I presume "ים" is best for all these. Then there's the Sargasso Sea in the Atlantic Ocean, but these are proper names so you can't change them.
הַשּׁוֹטְרִים מְחַפְּשִׂים אוֹתוֹ בַּיָּם (וּבְאוֹקְיָנוֹס) וְהוּא בֵּינְתַיִם בְּמִסְעָדָה עִם יָם שֶׁל בִּירָה בְּתוֹכוֹ. פָּשׁוּט - אֵין יָם כְּמוֹ יָם...
That's an accurate distinction, but in English we would usually just say that the police arrived; it is less common to hear "the police officers arrived"
Could this search even include looking for him in a lake in the forest (in a pool of fresh water) and not only in the salt water (the sea)?
No. ים is very specifically the salty one. Lakes are not included.
Historically, a few lakes, the Kinnert (sea of galillee), the dead sea and the Caspian sea are sometimes referred to as ים, but those are misnomers as they are inland bodies of water. It does not extend to other lakes. It is also not common to say even about them "אני הולך לים"