la_carrenio2003,
Since you mentioned it, the correct English terms for the three main sections of classical sonatas are "exposition", "development," and "recapitulation."
Your are correct in saying knowledge of theory is very important in interpreting music.
bachopoven,
Music theory is not just chords. It also involves formal design of music - sonata allegro, rondo, etc. - counterpoint, voice leading, etc., etc., etc.
Put together, they are the tools composers use to create the works of art that we play. The more understanding we have of what the composer is doing, the more we can get inside a piece of music and understand it.
The answer to your question "Is most music written in the known chords/arpeggios?" would have to be yes. With very few exceptions music theory and especially harmony does not pre-date its application. In other words, different harmonies were not first invented, and then composers wrote music applying those invented harmonies. The reality is composers wrote music using - for the most part - common practice harmonies, and music theory grew out of the music composers wrote. (there are a couple exceptions to this - the second Viennese school, and the Florentine Camarata - but for the most part, what I described has been the overall model).
So, if you accept what I just said, the logical conclusion is since composers using harmony in a particular way pre-dates its description - or prescription - as theory, then for the most part music is written with "known" harmonies.
You can take that idea, and extend it to formal design as well. For example, there was no theorist in the 18th century who said "OK all first movement of symphonies, sonatas, and chamber music should have an exposition with two contrasting themes where the second theme modulates to the dominant, and then there should be a middle section where the aforementioned thematic material is developed, followed by a recurrance of the two themes, this time with the second theme in the tonic - coda is optional." The fact is, sonata allegro form evolved, and what we read about it - in terms of its structure - is simply a description of the final stage of that evolution - not some sort of rule book 18th century composers were working from.
Knowledge of theory and harmony can be a wonderful help to you when learning and memorizing music. Also, it can help you interpret music. For example, would you play a dominant chord the same dymanically as a tonic chord? Or, how would understanding of sonata form, and the fact that the climax occurs in the middle of the piece make you inetpret the music differently than you would if you had no understanding of it?