Rotation sites are determined in your 2nd year, usually by mid-December. It is done on a lottery system. You pick your 3 top choices for locations and then if they pick your name first, you get your first choice (yeah!!). If your first choice is gone by the time they draw your name, you get your second choice, and so on...
This year 75% of the 2nd years landed their first choice (out of a class size of 250). I believe only 10% did not match at all, but don't hold me to this number. If you don't match you go through the lottery process again with the other students who didn't match, and you choose from the sites that are left.
I understand that it is wise to not choose all of your sites that only have 2-3 students per site, or sites that are extremely popular like Kansas City or Florida. So it might be best to choose one "popular" site and 2 other sites that are good, but also easy to get into (statistically speaking) because they take more students (like Ohio or Detroit).
You can do all of your rotations at one site if you wish. I think most students try to do at least one elective at another location, just for the experience or maybe because another location will have a specialty they are looking at going into. I really think UHS has a great lotto system compared to some other schools. Some schools have students scrambling for rotations, which might end up at a less than desirable spot.
I can't comment on if the class of 2007 is full- best to call admissions and ask them directly. They did a bunch of interviews today, so I have to imagine they are still filling spots.
Good luck.