I hope you can see that the first difference between answer choices is how the portion after "Europe" is constructed.
In A, C, and E it is treated as a modifier, and in B and D it is separated by a semicolon and therefore begins its own clause.
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E. Europe, which is a situation that has long frustrated American furniture executives and trade negotiators and has become
Let's begin with the lowest-hanging-fruit of all modifiers, the "which" relative modifier in choice E. When "which" (or "when" or "where") is used, the modifier must modify the immediately adjacent noun. But "Europe" is not logically "a situation that has long frustrated American executives" so choice E is therefore incorrect.
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C. Europe, long frustrating American executives and trade negotiators and is becoming
Choice C is problematic in that the two -ing verbs perform different functions: "frustrating" could properly serve the purpose of a participial modifier at the end of the sentence, but the "is" before "becoming" means that "becoming" is used as a verb and not as a participle/description. This then rules out choice C.
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A. Europe, a situation that has long frustrated American furniture executives and trade negotiators and has become
While on the topic of modifiers, be sure that you recognize why "a situation that has long frustrated..." is a properly-used appositive modifier here.
When a noun phrase (such as "a situation") is used in the beginning or in the middle of a sentence as a modifier, it must modify the immediately-adjacent noun. But at the end of a sentence, as "a situation" appears here, that appositive phrase has the leeway to modify the entire preceding clause. Here that modifier is correct.
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B. Europe; this is a situation that has long frustrated American furniture executives and trade negotiators and becomes
D. Europe; this is a situation that has long frustrated American furniture executives, trade negotiators, and is becoming
Choices B and D each separate "the situation" with a semicolon, and that is perfectly allowable in this case. But each commits an error in a different place: in B, the error is the verb "becomes," as in "this is a situation that becomes..."
Because the verb tense of the situation is already set as ongoing ("has long frustrated") and because the idea that this one situation "becomes" (seemingly over and over again, when really it's just one action) is illogical, B is incorrect.
With choice D, the lack of the word "and" between "executives" and "trade" sets up a three-part list, which then fails when the third item is not a noun, but rather a verb "is becoming." Answer choice
A is therefore correct.