The first part of your 2nd sentence is perfect :D The second part would be: "but also doesn't do her homework at all." Not only...but also is the correct structure. So the full sentence woud be: "Not only does she not learn new words, but also doesn't do her homework at all."

First is incorrect and unclear. Second ok, as corrected by others, but not too natural. She neither learns new words nor does her homework. (They are two separate things. But ‘learning new words’ is an odd thing to say without context.) She doesn’t do her homework and therefore doesn’t expand her vocabulary. (One thing) She neither studies her vocabulary list nor does her homework. She’s not studying her vocabulary words and not doing her homework. (In speech, both neither/nor and not only/but are rather formal. In this phrase, we’d emphasize both ‘not’s.)

With the activity "homework", you want to use the verb "do." He does his homework. I do my homework. They don't do their homework. She will do her homework. Do you do your homework every day? Is he doing his homework right now? Good luck!