Anchoring the organelles in place, the tasks that are performed by the cytoskeleton within a cell's structure are crucial, and composed of microfilaments, intermediate filaments and microtubules, it maintains cell polarity.
A.the tasks that are performed by the cytoskeleton within a cell's structure are crucial and, composed of microfilaments, intermediate filaments and
B.the cytoskeleton performs crucial tasks in a cell's structure and, composed of microfilaments, intermediate filaments and containing
C.the cytoskeleton performs crucial tasks within the structure of a cell and, composed of microfilaments, intermediate filaments and
D.the tasks being performed within a cell's structure by the cytoskeleton are crucial and, composed of microfilaments, intermediate filaments and
E.the cytoskeleton performs crucial tasks within a cell's structure and it is composed of microfilaments, intermediate filaments and

A - Incorrect. The original sentence begins with a modifier: Anchoring the organelles in place. A modifier should be placed right next to the noun it describes. In this answer choice, what immediately follows the modifier is tasks. Even without any knowledge of cell biology, it is clear that this modifier cannot logically modify the noun tasks as a task cannot anchor organelles or do anything, for that matter.
B - Incorrect. Although this answer choice corrects the original Dangling Modifier error by placing the noun being described (cytoskeleton) directly after the modifier describing it, it creates a Parallelism error. The first two items in the list at the end of the sentence are nouns (microfilaments, intermediate filaments), but the last item is an unconjugated verb (containing). In a list, all the items must be in the same part of speech and/or of the same kind (all verbs or all nouns, or all adjectives...).
C - Excellent work! This answer choice corrects the original Dangling Modifier error by placing the noun being described (cytoskeleton) directly after the modifier describing it (Anchoring the organelles in place).
D - Incorrect. This answer choice repeats the original Dangling Modifier error.
E - Incorrect. Although this answer choice corrects the original Dangling Modifier error by placing the noun being described directly after the modifier describing it, it does not fit into the original sentence because it disconnects the clause it maintains cell polarity from the rest of the sentence.

The problem is that the clause "it maintains cell polarity" is unconnected to the rest of the sentence. Main clauses should be connected by conjunctions such as and, because, although, etc, and E misses that linking word.

In the correct answer choice the last clause is connected by the and after "cell" (the cytoskeleton performs tasks...and it maintains cell polarity) which leads to parallel construction composed of A, B and C. The parallel construction ends with microtubules, and acts as a modifying clause which modifies the subject of the last clause "it".