In choice (A), the word "and" makes the sentence ungrammatical. The modifier "works which enjoy a widespread popularity in America" modifies "paintings" and does not otherwise affect the grammar of the sentence, so we can imagine it omitted. Then we have the ungrammatical phrase, "Norman Rockwell's paintings and becoming popular." We can eliminate choice (A).
In choice (B), we do not have the basic subject/verb pair that every sentence requires, because there is no verb for the subject "paintings." The word "reflecting" is a participle (it begins a modifying phrase) and does not form a predicate of the sentence without a linking verb, such as "is." We eliminate choice (B).
In choice (C), the singular verb "reflects" does not agree in number with the grammatically plural subject "paintings," so we eliminate choice (C).
Choice (D) is clear and grammatically correct. Choice (D) is clear and correct. The subject "paintings" matches the verb "reflect" in number (plural) and the tense is correct; since we are talking about a general statement, we use the present tense.
Choice (E) has a problem similar to that in choice (B): we do not have the basic subject/verb pair that every sentence requires, because there is no verb for the subject "paintings." The word "which" introduces a modifying clause, which is not part of the main clause and can't supply a verb to the main clause. We can eliminate choice (E).
The correct answer is (D).