Is "δικηγορίνα" used in this case for a female lawyer?
Too, really too colloquial, but correct.
We (females) do not prefer it. :-[
Does it sound like belittling, condescending?
Yup, you got that right. There used to be other "female" words that sounded that way but slowly they are being rejected. Something like we don't us "actress" or "waitress" in a lot of places....where I come from for example.
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.