Which statement best describes the role of dialogue?

dialogue defines key terms and vocabulary.
dialogue provides researched facts.
dialogue offers descriptive language.
dialogue develops characterization and mood.

The answer is: Dialogue develops characterization and mood.

Dialogue is a literary device or technique that an author may employ for several purposes, although, the most direct purpose is to straightforwardly present the character as he speaks and thinks in order to explore the depth and constitution of the character in question which sets a mood and a flow for the reader to be more closely acquainted with the character and the story´s plot.  

faulty parallelism is a grammar construction where there is no balance in the parts of a sentence they have a similar meaning but the grammar structure is not equivalent.

the correct version of this faulty parallelism in the sentence is:

jefferson wrote the declaration of independence, and he was the nation's third president.

the problem with the first version is that the sentence:

"jefferson was both the writer of the declaration of independence"

presents jefferson as both a subject and an agent for the verb "write" because if he was "the writer" then the declaration of independence was written by him, besides that fact, the sentence presents a dependent clause.

while the second sentence:

he was the nation's third president.

presents a basic subject+verb+object structure

so, to give a proper balance to the structure, or better said, to give a parallel structure, we must write a basic s+v+o structure in both sentences:

jefferson wrote the declaration of independence, and he was the nation third president.