No athletic scholarships in the Ivies.
Recruited players have a special path through admissions; if they get over the academic bar, that's good enough.
Walk-ons have the same path as every other applicant. The advantages which may be available to them (e.g., child of an alum, sibling, developmental) are the same as for every other U.S. student. That means essays, LORs, scores, ECs, and the rest must top virtually every other applicant.
Ivy teams have those walk-ones. A coach telling a kid that there is a space for him on the team if he gets in will have a spot waiting - because at virtually all, if not all, the schools the roster doesn't max out.
As for playing time, whatever is earned is earned. Very even opportunities given to every player to perform. Best player wins time.