You can get a vacuum at almost any time from the RA on call. They'll meet you by the offices at the main entrance, and you give them your student ID and get the vaccum. You'll get your ID back when you return it. The main thing I would recommend bringing for cleaning purposes is dishwashing detergent, since there isn't always communal stuff in the kitchen.
Not on a regular basis, but most people use the microwave or boil water for tea/coffee pretty often. If you like to cook, you'll definitely have fun. One time my friends and I went out and bought food, and the guys cooked delicious filet mignon and tortellini and vegetables for twelve people.
No, bring your own vacuum. I got a $10 one from Bed, Bath and Beyond. My RA was so unpredictable about when she'd be in, and other people would always be borrowing the vacuum and not returning it promptly. No joke, I think bringing it was the best thing I brought. Much more useful than the tons of books/DVDs that I never ended up touching because I was busy doing work and such.
Ceruleanyankee, did you live in Dickson? I'd say it depends on the dorm. Even if it's only $10, you might not want it taking up space in your room. Clara Dickson's RA staff is incredible. I never had to wait, and there are honestly 5+ vacuums sitting in the office. Plus you're not going to get one that's as good as the industrial ones you can borrow.
No, I lived in Balch. But my vacuum was really small and light - a standup, but one of those travel ones (not like a huge one or anything). Dickson might work differently; you're right, I can only speak from experience.
If you bring a vacuum and live in Dickson, I can guarentee that people will be knocking on your door at all sorts of odd hours asking to borrow it. As word started t spread, I even had people I'd never met from different floors asking to borrow my little vacuum...including my RA.