Admissions looks for candidates who are physcially fit, have demonstrated leadership, and are academically sound. Being a successful athlete generally indicates some degree of aptitude in two of those three areas.
If you mean at the Academy, it's really more an emphasis on "get out and do something active as part of a team," which is sensible in a military school. If you wanted to go out for varsity whatever, great, but you had to do some kind of extra-curricular activity, whether it was football or sailing or band or intramurals or whatever.
No. Your physical fitness grade does factor in to your order of merit, but that's only your PFA scores. No one gives a shit if you were varsity whatever when it comes to service assignment.
If anything, the varsity FB guys were often so banged-up by Firstie year that they couldn't commission in URL, much less NSW or aviation. At least amongst guys who got SEAL billets out of the Academy...basically they want high grades and super fit. I knew a guy in my class who really, really wanted to be a SEAL and was a PT animal - would swim to the Sea Bouy and back for giggles on Saturday mornings - but his grades weren't hot at all. It was made clear to him that NSW wasn't in the cards. As far as what they do look for athletically, they tend to recruit more from triathalon/Iron Man and water polo types - endurance athletes who are comfortable in the water. They get a lot of time to look at Middies who want to go to BUD/S. They run a lot of indoc/screening events over all four years, culminating in Mini-BUD/S, and the opinions of the Team guys assigned to the Academy are given a lot of weight.