I have seen a lot of wrong explanations here.
A problem with SC is that a lot of people get the answers right, but it they don't get it right the correct way. In fact, this SC has more do with logic than with Grammar. Infact, there is hardly any grammar involved here.
Let me explain a few incorrect explanations first:
For example, someone said that he/she ommited Option "A" just because the word "each" was followed by singuar "has". This is not correct as "each" is a singular and in this case it clearly refers to a singular noun.
Another explanation, mentions that Option "A" and Option "B" are not parallel as the options' two clauses use different verb "are" and "has". Two clauses can be parallel despite having auxiliary and transitive verbs.
The errors in Option "A" and "B" lies in the subtle endings, which are infact wrong comparisons. I will explain them using logic and commonsense.
A)independent, and each has only a peripheral relationship
with the other. What other? The message is not clear, is clause talking about relationship of three plays with one another or relationship with some other plays.
B)independent, and each has only a peripheral relationship
one with another. Again suspect of not giving a clear comparison. Which another? Is it talking about the three plays? or some another play?
C)independent, and they have only a peripheral relationship
with the others Same problem as A's.
D)independent and have only a peripheral relationship
with one another. Correctly makes the comparison with the three plays.
E)independent and have only a peripheral relationship each
with the other. Same problem as A's