That may be true for you, but I am not the least bit unsure of whom I am attracted to. As for "what sex they're supposed to be relative to", I'm not sure what that means but the standard of "supposed to be" doesn't have to apply to anyone unless you want it to.
No, those terms have well-established definitions; not ambiguous at all.
That's sexual preference, and not the same thing as sexual orientation. For most of us sexual orientation and sexual preference match up, but that doesn't make the terms interchangeable.
I believe that your therapist is correct; sexual orientation does not change, or at least not often. In your case, your sexual preference stayed the same, but by definition your orientation changed. Now you're a lesbian, before transition you were not.
In my case I was heterosexual before transition and I still am, but the gender of my partners has changed.