Hi, I can try to help. Brown is a great school to aspire to (plus it is in my home state of RI). What you have written so far under the first question is excellent. Expand on these concepts, with your word limitations.
For the second essay:
Brown's curriculum provides the privileges and independence I need to flourish: I could become engrossed in my major, yet still be at liberty to become fluent in French or lost in Aristotle and Sophocles' worlds of philosophy. Say "I will become engrossed in my major."
This sentence is a bit too long, does the curriculum provide independence? Or is there a better way to say this? I would add this: the college want to hear about your plan. Emphasize the fact that you are a person with a plan. Link the college skills you will obtain to your future plans. Talk about your short term goals as well. You are off to a great start, good luck in school!
One more thing that I forgot to mention. Explore the city of Providence online, if you are not from the area. Living in Rhode Island is very culturally stimulating, there are many museums, libraries, attractions, and events, all within walking distance of the school. The city of providence has all kinds of people, and has fantastic restaurants, shopping, and nightlife. Most students in the city seem very comfortable, and the location of the campus very close to everything you could possibly need. My uncle graduated from Brown, he says it is hard to get in, but once you attend, it can be a breeze (prob because the classes and environment are so enjoyable). :)