One of my favourite k-drama is 365: Repeat the Year
There are multiple words to describe a character that is never developed by the author. A flat character, for example, is a character that is only defined by one or two traits and nothing else. However, in this case, I think the answer would most likely be a static character, which is a character with little to no development so as not to take away from the story being told.
Yes it should because then the reader can get a good image