I think here "linguae" is in the dative case, which also ends in "-ae" for the first declension. The verb "studere" can also use a noun in the dative form, in this case the meaning would be "many women dedicate themselves to (the study of) latin".
I think you are right. "linguae" could be Gen. Sg., Dat. Sg., Nom. Pl. Nothing makes any sense. What do many women study? Acc linguam
"Many women study a language" was marked incorrect and corrected to "Many women study the language"
I had the same problem and reported it. I imagine it'll be updated soon.