DivI (including Stanford/Northwestern/Duke) and Ivies can generally guarantee you a commitment if you hit some benchmarks. You also have to be a good player. DivIII is a softer process, but the admissions boost is also softer.
Well, none of the schools you listed have letters of intent because they don’t award athletic scholarships. If they are contacting you, or if you fill in the ‘recruit’ form on the website (it did work for my daughter), you’ve got a foot in the door. If you have a club coach or high school coach, the schools will contact you through the coach; you are too young to be contacted directly by a coach.
Go to the NCAA websites and watch the clips about recruiting, what schools can offer what. Yes, the big thing the Ivies or the LACs in New England can offer is admission help. Research the teams, coaches. If you are going to any tournaments or showcases this summer, send the coaches your schedule and ask them to watch you.