Which are not ever justified
The presumption is that society needs a defense against those motivations, and soldiers volunteer to protect their society or people. It is not their responsibility to determine which orders to obey or what wars to fight, but by the same token, their understood position of obedience to their appointed or agreed upon leaders makes them valid targets. Their volunteering constitutes a tacit agreement to abide by certain conventions. Arya is not a soldier, has never enlisted in an army, and does not announce herself as a valid target by wearing a uniform or banding with fellow soldiers. She takes life because it suits her wishes, and that is always wrong. The most justified killings she committed were of the most innocent individuals - the stableboy who thought she was bad and tried to capture her, and the Bolton soldier on her departure from Harrenhal, who was merely doing his duty. Because those were direct issues of self-defense and liberty, she was justified. Arguably, the first murder she selected for Jaquen was somewhat justified, but it was not her place to single him out, much less kill him alone out of so many others who deserved it equally. She even KNEW whom she SHOULD be selecting if we are going to use your ridiculous formulation of equating a pre-pubescent civilian child with a soldier, and chose instead victims who arosed her pique.

In the first place, Arya did no such thing. She ordered the murders of a soldier and servant, who to the best of her knowledge had never borne arms against House Stark and were certainly not in King's Landing when her father was betrayed and killed. She murders a man who fled an unjust fate in the Seven Kingdoms, and while he might have been a jerk, was not in the least deserving of death, except by a legal technicality. If he is going to die for such a reason, it must be done by good and lawful means. There is certainly no indication that Dareon is going to harm anyone in the future or any similar reason to justify his death on the grounds of necessity. He is only liable for death because of a Seven Kingdoms law, and therefore, only a duly empowered representative of the Seven Kingdoms government or legal system has the right to kill him, and only in accordance with their laws and rules. The King himself or his Hand would not have the right to slit Dareon's throat in an alley or stab him in the back and steal his boots. A girl hiding behind the civilized conventions which protect her from reciprocal or preemptive attack that is justified against soldiers, has NO right to take upon herself the privilege and duties of Seven Kingdoms justice.

In the second place, you are proceding from a false assertion of the justification of the soldier. A soldier is NOT justified in killing innocents or civilians "to rectify a wrong against his country." He is justified in killing enemy soldiers, not because of what they may or may not have done, but because they have volunteered or agreed or been compelled to obey the orders of an enemy of his country, as determined by the authority to which the soldier has submitted. The theoretical uninvolvement of his "vicitms" is disingenuous, since by putting on the uniform, or taking the shilling or bearing arms in service of their leaders, they have made themselves liable as an instrument of that leader's will. If that leader is an enemy, than a soldier or anyone in service to the power or polity who considers him such is justified in fighting and killing those aligned with him.

Risking your life for others is an irrelevant comparison with one who takes life for personal satisfaction?

Depending on his ability to do anything about it, maybe. In order to best effect a defense of his country or cause, however, a soldier agrees to trust in the leadership of his country or cause or military organization to determine what the best interests of the country are, and how the security thereof is best protected. To challenge the leaders over every little possible quibble or legal technicality undermines the very purpose for which moral allowances for a soldier are made. On the other hand, there are orders or policies or leaders who are and can be recognizably evil. But what if their enemy is evil as well, or if your country has an evil leader but is attacked? A soldier has to make his decisions carefully in such cases. An Iraqi cannot be faulted for defending his country no matter his opinion of Saddam Hussein, or a German regardless of what Hitler may have done, or Russian under Stalin. A soldier who is conscripted is facing punishment for disobedience and can hardly be faulted for killing even good men who seek to do him harm because of the uniform he is wearing. On the other hand, none of that justifies committing murder, rather than militarily justified killings. The murders of prisoners by German soldiers from 1939 on, despite long-standing and well-known agreements by their country to do no such thing, are in no way justifiable, for example, or the rapine and destruction perpetrated on German civilians by Russians invading Germany at the end of the war, no matter that they had the tacit approval or overt encouragement of their leaders.

Not automatically because she has taken life, but because of the circumstances in which she does so. She is not remotely, in any circumstances, under the protections and exemptions of a soldier in the line of duty, or the position of a person defending herself from attack or threat of loss of life, liberty or property.