So does this just mean "live" in the sense of residing somewhere? Or is it also the "live" in the sense of being alive? (Not in this context obviously, but the verb in general.)
Yes, it's just like "to live." When paired with a location, it means "to reside somewhere", in other cases it means "to be alive".
Is "Zsuzsa hol lakik?" correct as well? What is the difference between lakik and él?
Él sometimes does, lakik always does mean "to live" in the sence of "to reside somewhere". Should be an acceptable translation for "Where does zsuzsa live?".
It's either "Hol él Zsuzsa?" or "Zsuzsa hol él?", but the verb and the interrogative pronoun can't be separated.