Hi - I will get to your criteria however first, a preamble. How you define what "the Vietnam War" is really sets how you look at the whole issue. If you look at it as an attempt by the "North" to attack the "South" backed by the Chinese Communists your answers above tend to come out in favor of the US action, particularly applying the first set of criteria.
However, I really think you need to see it in context. From 1905 onwards Vietnamese nationalists sought independence. This was largely a peaceful movement. These independence movements were suppressed with a great deal of brutality, and not a lot of justification. They became more radical and the first Communist elements started during this radicalisation process in the 1930's.
During WWII the Japanese invaded and retained the French administration. (France was ruled by then by the Pro-German Vichy regime.) The French / Japanese acted barbarically and millions of Vietnamese died. The nationalists started fighting the Japanse as well as the French. The western powers made a deal with the Vietnamese independence movement that if they helped fight the Japanese they could be independent after the war. (Note, the persons who gave this impression had no real authority to do so.)
In 1945 with the fall of Japan the independence movement declared a government by the Viet Minh, a coalition of all of the nationalist independence forces. This was strongly influenced by communist elements.
At this point the war time promises were forgotten and the Western powers used the same forces that had been fighting for the Germans (including re-armed Japanese POWs) to get fight the nationalist Government. Now, the legitimacy of this Government was pretty dodgey - however it clearly had popular support and in the power vacuum was no less legitimate than any other.
Not surprisingly, the Independence fighters decided that the West could not be trusted and turned to the only alternative - Communist China & Russia for help. This cemented the communist influence in the new Government which (due to the deep seated historical distrust between Vietnam and China) was by no means a forgone conclusion until that point.
France set up a puppet Government in the south and a general uprising followed. Both governments claimed to be the true government of Vietnam.
The Communist countries recognized the (Northern) Vietnamese state in 1950, and from that time onwards the US started to get involved in support of the French. (first Indochina War).
By 1954 the French had been comprehensively defeated (look up Dien Bien Phu) and during a peace conference in Geneva Vietnam was temporarily partitioned between North and South. It had been agreed at the Geneva conference that there would be a general election and the country as a whole would choose its future.
The Americans knew that the majority of the population supported the Communists (whom they saw as their liberators) and therefore backed a separate regime in the South which declared itself to be a sovereign state and refused to participate in the election. In 1955 the Southern regime started to wipe out the Communist opposition by torture and execution. This led to armed resistance by the Communists backed by the North and by China.
The Americans intervened in support of the southern regime and what the US sees as "the Vietnam War" (second Indochina war) kicked off.
Now, obviously I think that the Vietnamese people to that point had been badly scr3wed, and right or wrong the northern government had more claim to legitimately rule the country. There was no historical justification for a "North" and "South" vietnam and although it had some support the Southern regime was corrupt & brutal. If you therefore look at this as the end of a long conflict, rather than the start of a brand new one your criteria above look very different.
Applying my perspective I have the following view. Sorry - this is going to be no more than an opinion, but that is all you can really get after all.
1. war started and controlled by authority of state (on both sides)
Yes, certainly by the North. The point where a revolutionary regime becomes a "state" is a bit of a grey area, however by this stage (1960 or so) it would be hard to argue that the North was not a state. The legitimacy of the South as a separate state was a bit more problematic. I regard it as a foreign puppet state, however others disagree.
It was never just a war between North and South, however. The Viet Cong, southern insurgent revolutionary force separate from the North Vietnamese Army and therefore treated by the US as terrorists. However, if your village is being burned and your family tortured and shot, what are you supposed to do ?
I also dispute that a "Just" war can only be conducted by a state actor. If that were the case, the American Revolution, the French Resistance and the ANC's insurgency in South <
> balance of my answer is cut off. However, from my perspective of the history I guess you can see which way I would jump.