Is "δικηγορίνα" used in this case for a female lawyer?
Too, really too colloquial, but correct.
We (females) do not prefer it. :-[
Αυτή είναι ένας δικηγόρος was marked wrong because I shloud have used "μία" ?
That's right. Since it's "she" you should have used "μία/μια". Here is a guide with the names of female professions.