When a murder victim does not have immediate family or friends (or neighbors) to take the murderer to court, this right to take the murderer to court can be claimed by someone else. A lot of the rest of your questions are actually quite general to anarchy and not this specific case. For example: “If the murderer is caught, what happens to him?” Well, what happens if the murderer murdered a middle class family man? Is this murder somehow different?
I highly recommend Clayton’s posts What Law Is and A Praxeological Account of Law. That should help you on the track of understanding how a system of law might operate in an anarchic system.