How important is class rank for Ivy League Colleges, or more specifically to the service academies (ex. USMA)?

In order of your questions.

1.) Ivy League Colleges consider class rank very important as 95% of admitted students are typically in the top 10% of the class. So if your school has 350 seniors, ranks 1 through 35 would qualify as the top 10% of the class.

2. US Military Academies are not Ivy League colleges. While they are getting increasingly more competitive with sub-10% admit rates for Westpoint, Annapolis, and Colorado Springs, rank is not as important as it is at Ivy's (except for Air Force). The Coast Guard is the least competitive of the military academies.

Side note: Earlier this year affirmative action was rolled back at all colleges except for Military Academies. So the argument is that Military Academies want diversity because they don't want to graduate just White or Asian officers who have superior grades and test scores because on the battlefield there will be a disproportionate amount of black and brown troops to lead. Therefore they feel that if they are led by persons who look like them and have similar backgrounds then they will be more effective and successful in arenas of combat and missions. Nevertheless, WestPoint is being sued for using Affirmative Action by the same group of people that sued Harvard and UNC. Therefore if you are black or brown, your race will be a big boost for the time being if you apply to US Military Academies. It might get rolled back next year when the Supreme Court hears the oral arguments and takes a vote on it.

Good luck.