Eeep! Lots of questions!
The UN has both worked and failed on different levels. UNESCO and UNICEF, for instance, do a lot of good work. The body can and does co-ordinate relief efforts in time of natural disaster, etc.
Beyond that, however, the UN is a talking shop and a paper tiger, its' varying resolutions and International Criminal Court decisions either implemented or ignored depending upon the attitudes of the various nations involved. The primary problem being that the offending states and their allies remain voting members of the Organisation, making punitive action almost impossible.
In the past, when international organisations were called Empires, prompt and decisive action against aggressors could be and was taken. But the UN is no empire, has no armed forces of its own and nobody to decide when and where they should be deployed, and with what RoE and level of forces. Once the shooting starts, the UN can do nothing.
Unfortunately, no amount of reform would help. If the UN were to exclude certain nations from membership, or be enabled to suspend their membership, it would then be 'choosing sides', making it effectively a tool of its most powerful members. It's best role woud be to provide a neutral space for negotiations.
In the matter of the United States, its immense wealth and power make people tend to forget that it is by no means a mature nation. It takes longer than 248 years to build a nation, especially from such a hotch-potch of ethnicities, cultures, economies and environments. The US is not in any kind of decline, it is in fact still forming itself. Like all young nations, it is inherently unstable and may be entering into a period of fragmentation. Whether one nation, or several, are eventually formed remains to be seen.
Totalitarian regimes, aggressive empires, barbarian hordes, all part of an unending cycle. Educated, tolerant and hedonistic societies fall before ignorant, ascetic, intolerant ones. Unless the West can restore some of the barbarian vitality that led us to conquer so much of the world, then we will fall as Rome did.
Neither Iraq nor Kuwait had nukes, it's that simple. You tend not to go to law against a neighbour who is ready, able and perhaps willing to burn your house down with you in it! International law only applies to states that the sueprpowers feel safe in bullying.
Putin cannot achieve his aims legally. He doesn't want the Crimea and Donbas. He wants the whole of Ukraine, and he wanted to get it before they had a chance to join NATO. Any other countires in Eastern Europe who share borders with Russia and are not in NATO are equally in danger. So are all the former Soviet countries who are not in NATO or a similar organisation. Putin wants to bring Russia back to the same size and power as the old USSR. He is not entirely sane, and it would be foolish to expect him to act with either reason or restraint.
I don't think the Budapest Memorandum makes a difference. Putins' war is one of territorial acquisition, he is unlikely to use nuclear weapons in Europe, as the environmental effects would certainly spread to Russia. Nor does he wish to reduce Ukraine to a wasteland. The Ukrainians would no doubt be of the same view.
Practically speaking, there are only three scenarios in which nuclear weapons are ever likely to be used. A Russian strike on the US, because America is sufficiently far away for the effects on Europe to be minimal. By the Chinese on anywhere in Europe or the Americas, for the same reason. By Iran on Israel, because fanatics will not care about the millions of their Muslim brothers and sisters who would suffer, since it is for The Faith.
Ukraine can and did ask for NATO, or the EU, or the US, to establish a 'no fly zone' over its' territory at the start of the invasion. Regardless of any legal standing, the shooting down of a Russian military aircraft would be taken by Putin as an act of war. This would then have forced NATO to put boots on the ground in Ukraine. American leaders fear that this would lead to a Russian nuclear strike on the US mainland. So they told everyone else to say no to Ukraine. Nothing to do with law.
Ukraine is fully aware that any negotiated peace will lead to a significant loss of territory, its own demilitarisation and eventual transition ot a Russian puppet regime. Putin won't accept anythg that doesn't give him eventual control over Ukraine. His offensive is bogged down - he expected to overrun Ukraine in less than a month, I imagine - so there is no doubt that he would draw out any negotiations for as long as it would take to rebuild and augment his forces enouhg ot achieve victory. Which is why nobody is talking.
Trials could only take place in two circumstances. Either NATO enters the war and pushes as far as Moscow, gains an unconditional surrender, and manages to capture those responsible. Or, Putin is overthrown and his successors withdraw from Ukraine, end the conflict and hand the former leaders over. The current reluctance of any major power except the US to apply the death penalty means that Putin, if caught and tried, would spend the rest of his life in prison.
Ths is not the start of WW3. Russia, for all its supposed might, is bogged down in a war of attrition against one small country it should have defeated in days. Any chance of Russia getting anything other than a good kicking from NATO or EU forces is very small. There would be no use of nuclear weapons in such a war, one does not burn ones' own house down for thesake of burning the enemys'. China, following the teachings of Sun-Tzu will try to achieve thier agenda without war, which is seen as a failure of strategy.
But the Ukraine crisis has caused Germany to rearm. WW3 will therefore begin in the traditional manner, with a German attack on France. Under Angela Merkel, we saw ample evidence that, as far as Germany is concerned, the EU is simply the Fourth Reich. The UK has managed to get out, and it is only a matter of time before France elects a far-right or far-left eurosceptic government. Brexit has already left the EU scrabbling for cash. Frexit would leave it scrabbling for food as well, and the Germans can't let that happen. Besides, the entire history of Europe since 1803 has been the struggle for hegemony between France and Germany, and it continues today.
I only hope that this time, we in the UK have the sense to stay out of it!