China and the US are going to sabre rattle back and forth at each other for a very long time to come. We will see our battle fleets perform maneuvers near waters where China claims authority yet others in the area disagree, just as China will continue to push until they come to the brink of war only to then relent. For all of the seemingly hostile acts China takes, they've not directly (important word here) entered into war with another nation since WWII, and only did so because Japan invaded.
The US and China need each other too much, our economies are so grossly intertwined at this point that it would be both political and economic suicide for the two nations to enter into either a cold or hot war, considerations that never existed between us and Soviet Russia in the 1940s.
As for Russia, they're in Syria because they're an authoritarian people and they long for some semblance of the glory years of their Soviet empire, something most of their leadership still actively remembers. Every time the declared leaders of the world are upended, it creates a great deal of turmoil for the people. The Soviets are ousted from power in the late 80s and early 90s, conflict and hardship ensued during the transition. Current leadership has externalized their authoritarian need and applied them to other countries they see going through similar issues. Crimea wasn't happy with the fledgling Ukraine leadership, and there was military significance to the region, so Russia "helped" the situation by annexing Crimea and "stabilize" the situation. Syria's king has been challenged for more than three years now and the nation is in shambles with refugees pouring into Europe, so the Russians rush to the aid of the authority that they believe should be in charge. It helps Russia's national pride that it's also in opposition to the US in Syria, but that's just the side benefit to them.