I would never choose the ",and" to separate two verbs. Someone was trying hard to make this sentence sufficiently incorrect and one device they used was to separate two verbs "performed" and "published" with ", and." I will defer to the style manuals that have been cited as to whether this is ever permissible, but the following would not be correct on the GMAT - "Bob ran, and jumped." In this case (choice A), the comma is without a doubt intentionally designed to make this choice wrong.
Additionally, I would say that in answer choice A, "performed by the Duke's Company" is meant to be a modifier, yet there the form is not correct. You would need a comma or some other device to indicate the modifier, as in D, which says "Plays by Aphra Behn, performed by the Duke's Company, were published..."
This makes a proper modifier. Whereas A without the prepositions is "Plays by Aphra Behn performed by the Duke's Company, and published in England in the 1670s, made her one of the first female authors to earn a living by writing. So only the bold portions, "plays performed, and published made her"
As to the reasons that Paes does not like Choice D:
1) Paes, I have once again looked through the official material and there is nothing about avoiding changes to answer choice A. Do not say "the original sentence." There is no original sentence in terms of the underlined portion. There are only five equal choices.
Please see this example from the 1st edition verbal review page 240.
"Using a Doppler ultrasound device, fetal heartbeats can be detected by the twelfth week of pregnancy."
The correct answer changes the meaning completely by adding a physician.
"Using a Doppler ultrasound device, a physician can detect fetal heartbeats by the twelfth week of pregnancy."
2) Passive versus active should not come before grammar and clarity. Passive versus active properly comes after grammar, and the choice that sounds better in context. Choice D is certainly clearer and sounds better so active/ passive does not come into play. This is only a tiebreaker if all else is equal.
I hope this helps...