You're going to need to compartmentalize your private information much more than you've already done.

Do not tell him the schools you're applying to, the classes you're taking, the names of your profs, specific grade information, application status.

As for your current top choice law school, you might be able to spin this to demonstrate your professionalism in the face of an emotionally difficult issue. Email the admissions person. Briefly and unemotionally, inform him that your father has been exhibiting signs of cognitive decline, which unfortunately have begun to take the form of inappropriately disregarding personal, academic, and professional boundaries. It has come to your attention that he inappropriately contacted them, falsely purportedly on your behalf. Ask them to disregard any contact they've had with your father, and to understand that while you love him as a parent that his recent patterns of this type of behavior do not reflect on you or your own qualifications as a prospective student. End by politely asking them to please not disclose the process or status of your application to any third party in the future, including family members -- the admissions office should not have shared information with your father any more than he should have to some complete stranger who might have asked about you.

Your dad is almost correct about one thing, sort of, and that's this:

he has a right to post all the information he knows anywhere he wants.

It's not that he has a right, but he does have the ability. And he's demonstrated repeatedly that he will misuse this ability in ways that can and will undermine your future successes.

So what you need to do is to minimize the damage by limiting the information he gets. However much of this you want to explain to him is up to you, but you don't have to explain any of it. Given his inability to understand the damage he's causing you, it might be best to keep him in the dark entirely.