My answer is
(C). It took me 01:16.
(A) To convey correct meaning, "works like a common pacemaker" should not be parallel with "sends ... but remains" because the latter serves to illustrate the former.
In addition, while it is typical to see "X, Y, and Z" in parallel structure, the use of "X, Y, but Z" is not common partly because, in this structure, "X and Y(,) but Z" makes more sense.
(B) One way to see the sentence structure issue is to remove "sending electrical pulses to aid the brain when it is struggling to store new information", and the resultant text is not a well structured sentence:
The new device for aiding memory works like a common pacemaker remains quiet when it senses that the brain is functioning well.
(C) Generally Ok. The comma before "but remaining" is not really needed, but GMAT's adherence to strict punctuation rules is not airtight.
(D) "sends" and "remaining" are not parallel.
(E) No conjunction between "sending..." and "remaining..."
An alternative interpretation is that "remaining..." somehow modify "new information" (but the comma should definitely be removed, and the meaning is nonsensical) or "the new device" (but the distance between the two is too much).