Learn Danish: Kaptajnen og besætningen er længe til søs. - The captain and the crew are at sea for a long time.

This is a fossilized genitive ending. Hundreds of years ago, the Danish preposition til required the following noun to be in the genitive case, which ends in -s. Today, the case system is gone, but the -s survives in fixed expressions like til søs (at sea), til bords (at the table), and til fods (on foot).

Is there a difference between saying someone is til søs versus på havet?

Yes. til søs focuses on the state, activity, or profession of sailing and working on a ship. på havet is purely literal and geographical, meaning physically out on the ocean. Since the sentence talks about a captain and crew, til søs is the most natural choice.

Could I say i lang tid instead of længe in this sentence?

Yes, you can. Both mean for a long time. However, længe is a very common, tidy adverb for expressing duration with states of being, whereas i lang tid places a slightly stronger emphasis on the actual stretch of time. Both are perfectly correct here.

The word besætningen is used for the crew. Does this only apply to ships?

No. While besætning (related to the verb at besætte, meaning to man or occupy) is the standard term for a ship's crew, it is also used for the personnel manning an airplane, a tank, or a spacecraft.