1. Your perspective is valid. Both grammatical forms are correct. If we use the adjective "neat," it would modify the "written article," implying a clean written article. This emphasizes the cleanliness of the article's content.2. If we use the adverb "neatly," it would modify the past participle "written," forming a past participle phrase, and then would modify the noun "article." This means "a neatly written article," emphasizing the neatness of the handwriting.3. Based on the context of the short passage, it is about the importance of handwriting. Therefore, "neatly" should be used to modify "written" in this context.