How does the writer use grammar, language, sentence structures, the order of texts and layout to achieve effects and engage and influence the reader?
What a great question! The writer is akin to a divine being in a text. He or she can do many things to achieve different effects. Let me give a few examples.
First, word order in sentences is flexible. If we change the word order a bit, we can create emphasis. For example, we can say: "I love only you," or we can say, "You, only, you, I love." By putting the direct object first and the verb at the end, you achieve emphasis.
Second, because the way we think is usually linear, by placing certain episodes next to another, we make the human mind see them as related. For example, in John 12 Mary washes Jesus' feet with costly perfume and some criticize her. Judas is the spokesperson here. In the next chapter Jesus washes everyone's feet. The second foot washing validates the first one; it acts as a commentary on the first one. Writers do this kind of stuff all the time.
Third, with the advent of the modern book, the way a book looks also have a way of affecting the reader. We need to remember form is a conveyor of meaning just as content.
You ask a heavy question, so my answer will try to go to the gut, and that's the hook. One writes because it is their passion. A true writer doesn't just want to write, a true writer has to write.
The writer uses all the tools you listed, just as an artist uses different colors of paint, brushes, canvases, etc., to create his work. Lots of times writers use all these tools unconsciously. But I believe that author E.L. Konigsburg, had it right when she said that one has to know the rules before one breaks them.
In order for the writer to "achieve effects and engage and influence the reader," the writer has to be knowledgable of the "how-to's." Good writers use "proper language, sentence structures, the order of texts and layout" when appropriate and know or feel when to break the rules. Think of the language used in Gone with the Wind, any work of Mark Twain, Faulkner's The Sound and the Fury or Grace Paley's Enormous Changes at the Last Minute.
Bottom line: Ya gotta know the rules AND you have to have passion. A good writer is good because he or she writes well. A great writer writes because he or she has to in order to feel satisfaction, resolve a conflict, meet a need. It is a feeling writers knows...deep in the gut.
Hope that helps.