The discovery that Earth’s inner
core rotates independently of and more quickly than Earth’s outer layers is responsible for advancing studies of the flow of heat from the inner through the outer planet and of the formation and periodic reversal in direction of Earth’s magnetic field.Option Elimination - This question plays with our minds.

Long sentences, relative clauses, prepositional phrases, and SVs. If we stick to the basics, the question is comparatively easy.
(A) core rotates independently of and more quickly than Earth’s outer layers is responsible for advancing studies of the flow of heat from the inner through the outer planet and of the formation and periodic reversal in direction of Earth’s magnetic field.
Basic structure -
The discovery (subject) relative clause (which is a noun modifier modifying "the discovery") is (verb) responsible for advancing studies prepositional phrase (of the flow) and prepositional phrase (of the formation). Parallelism around "and". Ok.
(B) core rotates independently of and more quickly than Earth’s outer layers is responsible for advancing studies of how heat from the inner core flows through the outer planet, and the formation and periodic reversal in direction of Earth’s magnetic field -
The discovery (subject) relative clause (which is a noun modifier modifying "the discovery") is (verb) responsible for advancing studies of "the relative clause" (how heat from the inner core flows) and the noun phrase (the formation and periodic reversal). The structure around "and" is not parallel.
(C) core rotates independently and more quickly than Earth’s outer layers are responsible for advancing studies of how heat from the inner core flows through the outer planet, and how Earth’s magnetic field forms and the periodic reversal of its direction - SV issue.
(D) core, rotating independently and more quickly than Earth’s outer layers, are responsible for advancing studies of the flow of heat from the inner through the outer planet, and the formation and periodic reversal in direction of Earth’s magnetic field - SV issue
(E) core, rotating independently of and more quickly than Earth’s outer layers, is responsible for advancing studies of the flow of heat from the inner through the outer planet and of how Earth’s magnetic field forms and the periodic reversal of its direction -
The discovery (subject) noun phrase (the structure of a relative clause is broken) is (verb) responsible for advancing studies of "noun phrase" (the flow of heat from the inner) and of the noun clause (how Earth’s magnetic field forms and the periodic). The structure around "and" is not parallel.