It is confusing that sometimes when the German sentence is translated into correct English, it is wrong because an unnecessary word is omitted. Then when you translate literally, you are wrong, while the excepted answer is wrong. "The basement is standing under water" is not wrong" nor is "Water is standing in the basement".
I also think that your translations are good. They clearly conjure up the correct images. I don't see why a German idiom must be translated to an English idiom such as "is flooded" which is a moving target depending on what is "flooded". I suspect that translating "The bathroom is flooded" to "Das Bad steht unter Wasser" would be a questionable one.
It's an idiomatic expression in German - you can't always translate literally; you have to understand the meaning of the idiom. wataya explains below that you could also say (in German) "Der Keller ist überflutet" to mean the same thing.
You could also say 'der Keller ist überflutet'. 'Unter Wasser stehen' is an idiom that basically means 'being flooded'.
Is Stehen used to explain the state of an object? In this sentence the state of the object, the basement, is under water. Are there other examples of when you use Stehen to explain the state of sometime? Does Ein flugzeug stehe ins Himmel?