"She natively speaks Romanian."
Translation:Ea vorbește nativ limba română.
What does this mean? Does it mean that she speaks Romanian like a native or that Romanian is her native language? 'Natively' means nothing to me in this context. I've never heard it used.
That English sentence is indeed ambiguous and clunky.
"Ea vorbește nativ limba română" means that Romanian is her native language, but in English you wouldn't phrase it like that. You would instead say something like "She is a native Romanian speaker" or "She is a native speaker of Romanian". Of course you could also say it like this in Romanian: "Ea este vorbitor nativ de limba română."
If you want to say that she speaks Romanian like a native, then that would be:
"Ea vorbește limba română ca un nativ."
"nativ" being an adjective used as an adverb (hence invariant to the feminine noun)?
Yep. Now you know why the course authors phrased it using "natively" in English.