law suit

I am not sure if this has been discussed before, but I have some questions about the wrongful death suit against Walt for Barlow's death. Who filed this suit? It was said I think that the estate is suing. On behalf of whom? Branch is dead, Barlow is dead. Barlow killed Branch, he also paid to have Walt's wife killed. Then goes to Walt's house, with a gun, unloaded, but who would know that, ends up confessing to everything, then pulling the gun and being shot by Walt, and would have survived probably if he hadn't taken Walt's knife and stabbing himself to death. So how exactly is Walt responsible for wrongful death of Barlow.
I remember that Nighthorse said once that he owed him money or something, but who is actually suing Walt. And why. That doesn't seem like something that would even be seen in a court of law.

By the way, I am only up to Ep 5 in the new season, so I only know that he has a lawyer. I also thought it was weird that Walt would be upset that Cady can't be his lawyer, considering she is he daughter, and also isn't a lawyer who deals with that sort of case anyway.