No. No one has the right to commit murder — murder is illegal by definition. Perhaps you are asking whether ptsd can render a killer "not guilty by reason of insanity." only a jury can decide this, but in theory it's possible if the person could not tell right from wrong, or truly didn't know what he was doing, at the time of the act. States differ in their acceptance of the insanity defense.
A complex issue. I repeatedly tell my wounded warriers that ptsd is not an excuse for violence. But frankly, I have had patients with severe combate related ptsd become very aggressive in the middle of a flashback in which they were trying to protect self or others. It is a sad and complex issue.
Absolutely not. I have some involvement in criminal justice, and i hear the "abuse excuse" for irresponsible behavior -- from murder to wasting your abilities. It doesn't fly nowadays, "pop" claims aside. Ptsd is a grim thing -- my father survived the worst of wwii and was helped by treatment -- but even the most sympathetic psychiatrists recognize that you still know murder is wrong.