For me the answer to the question of whether abortion is right or wrong depends
Your questions raise a host of difficult issues. What gives anything a right to life? In other words, what in general (if anything) about an individual makes it morally wrong for others to end its life? I've never seen a satisfying answer to that basic question. Does an individual's right to life inhere in the individual, or does it instead depend on the individual's relations to others? Prof. Manter referred to "all the relational complexities that being persons entails." If by "persons" she meant "beings with a right to life" and if by "entails" she meant some kind of logical implication (and it's possible she meant neither), then she's implying that a right to life doesn't inhere in the individual. I'm not sure I'd accept that consequence. Suppose you become a hermit and totally disconnect because you're tired of other people. If you had a right to life before you chose total isolation, then I'd say you still have it, and it would be at least presumptively wrong for any of us to kill you. Or suppose you're the last human being alive on earth. If you had a right to life before the rest of humanity died off, you still do, and it would be at least presumptively wrong for an intelligent alien to beam down and kill you.
I should note that some philosophers explicitly reject your assumption that the morality of abortion depends on the ontological status of the fetus. Most famous among them is Judith Jarvis Thomson (see "A Defense of Abortion," 1971). According to Thomson, even if fetuses have an undoubted right to life, abortion is still morally permissible in at least the great majority of cases.