Oh, do the ropes course - it is a ton of fun and a wonderful way to get to know your classmates better. I was terrified too but had a fantastic time and was so proud of myself for doing stuff that I didn't think I could do. Also, you will not be pressured to do anything that you don't feel comfortable doing. If you don't want to climb something, you'll be given another responsibility, e.g. standing on the ground and holding the lines that keep your classmate safe up in the air. DO IT. It's fun.
White coat ceremony - business attire. Gals can wear pants/skirt with a nice shirt, or a dress. Pantyhose are optional in DC during August 😛 (It was 100F here yesterday with high humidity, ugh.) Guys should have a tie. No one should wear a suit, because you'd just have to take off the jacket anyway.
And here's more information you didn't ask about: there will be book sales during the first few days - don't buy anything in advance! I and my fellow MS-IIIs will be unloading a lot of our basic science books now that we've passed Step One (wooo-hooo). I remember adding up all the book costs in the orientation book and coming to a total of something like $900. Thanks to the used book sale I actually spent about $200.
Welcome to GWU!