Why is it OK to refer to things in the sea as being "under the sea"? Wouldn't that really be the sea floor and below?
"Under the sea" is short for "under the surface of the sea"; the phrase is meant to evoke the romantic image seeing the waves passing while standing on the deck of a ship, say.
If one looks out of the window of a train near the shore, one says "I can see the sea". That does not mean "I can see the sea bed" or "I can see under/inside the water", but "I can see the surface of the sea". Thus the word "sea" in common English usage means "the surface of the sea", and "under the sea" means "under the surface of the sea".
Similarly "underwater" means "under the surface of the water", "underground" means "under the surface of the ground", etc. etc.
At what point are you NOT under the sky? Where does the sky start? 5m above ground? 50m? 5000m? 50,000m?
Under the sea starts when you are under the upper most part of it.
An undersea expedition is anywhere beneath the surface.
Because you are below sea level.