Yes. My husband is biracial but he identifies as a black man, not only because that is how society sees him but also because of his experiences and upbringing. It's the same for many other biracial people.
Meghan has mostly referred to herself as biracial but as mentioned, she once corrected someone who said she isn't black. It really is a complex issue but ultimately, how one identifies is very much based on their own experiences, among other things.
Yes. Someone said "Meghan is not a black woman" and her reply was "My mother and I would disagree with you." Overall she is a very proud biracial woman but if you come for her blackness she will check you.