Regarding “demonstrated interest,” it matters significantly … in early decision! Binding early action or other early action items, like applying early for scholarships, are indicators to the school that a student is seriously considering attending. Really what they are trying to determine is the student’s likelihood of matriculating. Obviously, binding ER is the ultimate indicator. While not “demonstrated interest,” having a sibling attending or a parent alum has a positive correlation with matriculation. Anything that gives the reader increased confidence in the likelihood of matriculating are considered, as long as the applicant is qualified. Visiting the school? Probably not much, unless maybe if it’s referenced and leveraged in an essay.