I submit our Nation has not prevailed in a war since WWII. This has given our current enemies hope that they can exhaust and defeat us. I am intrigued by the idea that had we decisively defeated North Korea, would Vietnam have occurred? I believe that because we accepted something less than victory in Korea that our leaders have made our nation more vulnerable and emboldened our enemies in the present age.
Not sure about this thesis. The Cold War turned out pretty well for the U.S. Also proxy fights in Central and South America, as well as in Afghanistan, went pretty decisively in our favor even if the results weren't necessarily pretty for the inhabitants at the time. Also Desert Storm.

As for whether Vietnam would have occurred if Korea had been "won" --- not sure what you mean here. If by "win" you mean that the U.N. forces end up guarding the Yalu instead of the 38th Parallel? What about this scenario makes the Viet Minh give up against French colonialism or stops the U.S. from intervening in 1956?

Please provide evidence that destruction of large parts of China would have resulted in China giving up its backing of North Korea and assenting to a permanent U.S. presence on its border. The more likely scenario sees Mao and Stalin becoming closer and a much closer Soviet-Chinese bond.

Great powers can never lose a war; they must always be viewed as having won decisively.
Nonsense, unless your definition of "Great Power" starts and ends with Alexander the Great. The Romans suffered repeated defeats. So has every other Great Power in recorded history. Did the British Empire end with its defeat in the North American colonies?

Further, our weakness since WWII, I believe, has and will have significant consequences for the current world order. Should we lose in Iraq and elsewhere, who will view us as: 1. a reliable ally; 2. an enforcer of peace among the great powers. If I were Taiwan or Japan, I would not trust U.S. resolve. This is disastrous.
I remember similar doomsayings about Vietnam. Somehow Japan and Taiwan still remain independent and allied to the U.S., despite at the time facing a far greater and more ideologically implacable foe than al-Qaeda.