Deshawn turned his research project in a week early.
- simple
- complex
- compound-complex
simple

"Deshawn turned his research project in a week early" is a Simple Sentence.

Explanation:

Each simple sentence comprises a subject and a verb. A simple sentence always expresses things about a single action. In other words, it has only one independent (main) clause and no dependent clauses.

A complete sentence that states about a single action known as an independent clause. Whereas an incomplete sentence that requires an independent clause to get its sentence to get completed is known as a dependent clause.

Compound, complex and Compound-complex are the sentence types that use the dependent clause.

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the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.