Does this mean that she herself is asking or that she is giving a question to herself ;)?
Η ίδια εμένα η δική μου η θεία προσωπικά ρωτά τον ίδιο αυτηνής τον εαυτό της....
Η θεία μου την ρωτά (with accusative την) would mean "My aunt asks her" (implying: she asks a different woman), not "My aunt asks herself".
I think the form "ρωτάει" should be accepted. I have heard Greek people using it and you can also Google it.
Of course it is accepted...! Was it not accepted for you? Was it on a strengthen exercise?
There is a spelling mistake (ouselves) instead of ourselves in strengthening skills
This sentence does not contain the word "ourselves" at all, neither spelled correctly nor incorrectly.
ο εαυτός "self" is always masculine.
την εαυτή της would be a bit like "her selfess" :)