Rotators are designated between the four sites [UCH/Children's/VA/DenverHealth] for two weeks at a time. During my month, I spent two weeks at Denver Health, the main trauma hospital. There the majority of cases where Trauma, Hand, or Spine. At the VA, I experienced a mix of Adult Recon, Hand, and Sports. I'm unsure about the University Hospital experience. There was a rotator who was specifically assigned a sports rotation, though he might have had a inside connection beyond VSAS.
From what I understand, it is competitive to obtain a spot. With that being said, I don't think it is impossible. I hail from the south. My scores are solid, upper-middle class, but not extraordinary. PM me if you want further details. This is a place you'll definitely be given a chance show your worth, as you'll work hard and long. But the atmosphere is encouraging and the experience invaluable.
As to your previous questions:
1) Rotators are treated like a part of the team. We had specific responsibilities and were utilized throughout the day and on-call.
2) The residents and attendings were extremely approachable. They never seemed bothered by our presence, quite the opposite. Many times, the residents would buy my lunch, breakfast, or coffee. Had an attending take us for breakfast one morning when the first case was cancelled. I heard of them also taking the medical students for wings and drinks every friday.
3) Degree of participation is resident/attending dependent. At DG (Denver General), you tee up the notes with vitals, change dressings, collate the list before rounds, help with cases, manage the floor, and help out with consults. At the VA, you see patients in clinic, write up notes (must have VA access), present plans, scrub cases, tee up notes with vitals.
-tl;dr You definitely help out a great deal and they don't forget you exist.