In reference to the length of the essay, don't forget that thousands of these things are read. Hence, you have about 250 words to hook the reader before the eyes glaze over. While the other 250 words can sum up why you are special and an asset to Vandy, you need to sell yourself right up front.
Arts and Sciences has about a 1 out of 3 chance to be admitted without further qualification. You increase your odds if you apply ED but you may hurt yourself on aid. Tough trade off. You probably have a pretty good shot.
Music--talk to the school if you cannot visit. How many slots are available for your instrument--this defines how many admits they will have. They love marching band people. You may want to switch your choice of schools but you'll have to audition in person--can't recall if they'll take a tape. If you look at the stats they don't tell the whole story of how tough it is to get admitted into music. a great deal of applicants are voice majors--they may take 11 out of 100 applicants. don't know the stats for your area but you should ask.
Good luck. Great school. Great location. Great teachers.