I say the context would deter,one whether it was evil. Did the party get attacked in the bar and the bouncer joined the attackers and tried to kill the PCs? How do you think Conan would deal with that guy?
Baloney. If the bouncer tried to kill an unarmed person then that's attempted murder and the PC is justified in dispensing summary justice. If the PC attacked the bouncer then the bouncer was acting in self defense and doesn't deserve punishment.
Remember, this is D&D not Law & Order. I would have no problem with a PC killing murdering bandits out on the highways even if they surrendered. Killing bad guys is what D&D adventurers do, And if the bouncer attacked first then this situation is no different.
Yes. Very obviously evil. I dont understand how this is a question.
Killing bad guys in self-defense is what good and neutral PC adventurers do. Killing bad guys in cold blood is what EVIL adventurers do.
It would only be "in the process" if the PC had killed him during the combat, while they were both trading blows. Once the bouncer has surrendered, he's no longer trying to kill the PC (if he ever intended to do so), so he's not getting killed "in the process."In medieval setting? "He who grasp the sword, dies by the sword". He tried to kill the PC and got killed in the proccess.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.