-Hasn't she finished her homework already?
**using already in this sentence means you previously thought she had finished her homework, but just heard that she didn't actually finish it. You're showing that you thought she did, but you're probably surprised to find out that she didn't
As just a plain question with no hidden implications, use yet: "Hasn't she finished her homework yet?"
-I don't already know him
**I don't know him yet.