Would "Zsuzsa hol lakik?" be okay as well?
It is accepted now.
Yes, I believe.
Hol él Zsuzsa. Miért nem jó
Would "Hol lakik a Zsuzsát?" be okay as well?
No. Zsuzsa is the one doing the living - so she is not in the accusative case. And lakik is intransitive so can never have an object. You can "see Zuzsa" - but you cannot "live Zsuzsa".
No. (Hol lakik a Zsuzsa? can be)
So there may be a definite article before a name?
It's very colloquial. Don't do it, unless there's a modifier going with the name, like "little Zsuzsa" ("a kis Zsuzsa") or "old Ferenc" ("az öreg Ferenc").
Hol zsuzsa el?
I don't understand why it's not correct! :(
That's just speaking backwards. You can also say "Hol él a Zsuzsa?"
Focus! A question word always has the focus so MUST go before the verb.