Does Abortion Violate Rights? 

6:01 "Now, it is not always moral for a woman to have an abortion." This is where this video parts ways with Ayn Rand. Ayn Rand believed it is ALWAYS moral to act on an individual's rational self interest. Listing contrivances is unecessary. There is no requirement for special pleading for any exception to a principle. Abortion is always moral regardless of circumstance. It does not depend on receiving permission from a doctor who is personally concerned about risk factors.

You are correct to begin with defining the terms. "Liberties" are required actions for a self-directed means of survival. "Rights" are permissions of action given by an authority. In secular political societies, Rights are established when legitimate governments promise to use force to protect an individual's liberties. Having Rights begs the question, "by whose authority?" If government protects liberty, then Rights begin at personhood (political acknologment usually through birth certificate). If God protects liberty, then Rights begin at conception. If in a state of anarchy, then Rights do not exist whatsoever. Since there is no evidence that a God will intervene to protect individual liberties, it is correct to say that only governments grant Rights; protections of individual liberty.