I don’t know the rate of proxy vs non-proxy wars so I can’t answer that question. But let me give my opinion on the other points.
I believe that Taiwan is a part of China. It is officially called the Republic of China. I don’t know the details but I know they lost the civil war against the communist and Taiwan was the island they retreated to. It isn’t recognized as a country by most of the world because of China asserting its claim over it. I think many Taiwanese identify as Chinese and both China and Taiwan consider themselves to be the true China. The situation is complicated, I don’t know all the facts, both sides claim to be China, the US official stance is ambiguous, all I know is war with China is bad.
With regards with Russia and NATO. NATO has expanded it’s membership and each new member is geographically closer to Russia’s boarders. Russia feels threatened by this because they have NEVER trusted the west. I don’t know the history but this is what I picked up from watching documentaries on WW2 and the Cold War. Adding new members that are closer and closer to Russia was only gonna end badly because we tend to put weapon systems in those new NATO allies boarders. I think this is why Finland and Sweden didn’t join for the longest. It would raise tensions between nations.
Welp for reason’s only Putin and his advisors truly knows they invaded Ukraine and the reason stated is because of NATO’s aggression. I personally think things would have turned out better if Russia was more friendly with their neighbors and tried to established mutually beneficial trade agreements but I don’t know shit about international politics.
Am I presenting the other side to justify their actions? No. I think it is best to see the whole playing field when you are in a conflict.