Can one also say 'hur många timmar per vecka lära hon'?
No, lära usually needs an object or a particle of some sort, you could say something like ”[…]lär hon ut svenska” (lär is the present tense of lära), but ”undervisa” is sort of teaching as a profession.
How many hours does she teach in a week? > Is it similar
Same meaning. Though that sentence might translate differently, I don't know. But same meaning
Why "undervisar" doesn't need an audience or "i" here ?