My friend is living in Austria. He is wanted in Pakistan because he committed a murder. He wants asylum in Austria. Would the government there let him stay legally, or they would it deport him? Would he qualify as an asylum seeker or not?
Austria does have a bilateral extradition treaty with Pakistan. So the likely answer is yes, they would probably send him back (and not just deport him, but put him in shackles and send him back as a prisoner for the Pakistani authorities to take).
That being said, before Austria extradites your friend, it's likely to demand the promise from Pakistan that the death penalty be taken off the table.
Also, if your friend was unfairly persecuted for some reason, and if the murder was committed in self-defense, perhaps, there is a chance of asylum, but since we really do not know anything about his case, any kind of speculation, without having such information, would be futile on our part.