Hello!
I completely understand your frustration with idioms - they can be a huge pain to deal with!
If it helps, try to look at each option from the point of view of a person learning English for the first time. Idioms rarely mean exactly what the words convey. For example, we know in English that the idiom "cut a rug" means to dance, but to someone who doesn't speak English well, they think you're talking about taking a pair of scissors to a rug!
Let's look at each of these options, and what they literally mean to readers, rather than what we assume they mean:
Disease, pollution, and overfishing have devastated the bountiful oyster harvests that once sustained the residents of the Chesapeake Bay area.
(A) of the Chesapeake Bay area
This one makes the most sense from a literal sense. It is referring to people who live in the area we call "Chesapeake Bay." When we talk about people living near a landmark (mountain, river, bay, etc.), that's how we refer to them. Therefore, this is the correct answer!
(B) in and around the Chesapeake Bay
This answer suggests we are talking about people who live inside and around the bay itself. As far as I know, people don't live under the water in Chesapeake Bay, so this doesn't really make sense literally. We get what they mean, but it's not going to be clear to a person who doesn't speak English as their first language, which is why idioms are a problem!
(C) of the Chesapeake Bay
This answer also suggests that it's talking about people who live in the bay itself, rather than in the town/area surrounding the bay. We're not talking about people who live in boats on the water - we're talking about people who live on land around the area.
(D) around the vicinity of the Chesapeake Bay
Around and "the vicinity" are redundant - they both mean the same thing.
(E) living in and around the Chesapeake Bay area
This answer is wrong because it expands the actual location we're referring to. Instead of just people who live in the area called "Chesapeake Bay," we're now talking about people who live "around" or outside to too. This isn't true to the original meaning of the sentence, so it's a bad choice.
I hope this helps! I'm available if you'd like any follow up.