For your core rotations (IM, Surg, Peds, Psych, Neuro, FM), you'll most likely do them at a location affiliated with your school. That being said, some schools allow you the opportunity to do them at unaffiliated hospitals. So the best thing to do would be to ask.
When I was on my internal medicine rotation at St. Luke's (affiliated with BCM in Houston), I often worked with other medical students from other cities (UTMB in Galveston) and countries (Mexico).
Rotations are graded based on evaluations (subjective), shelf examinations and standardized patient practicals (objective). Scores (Honors, High Pass, Pass, Marginal Pass, Fail) often depend on percentile or score cutoffs. Again this varies among schools and even among different rotations within one school.