The US and the EU are some of the biggest consumer markets. If they for example implement a carbon price and levy import tariffs for imports from countries who don't this will have a big effect.
That would be more us versus them. China isn't worse than we (Europe and US) when we were "growing up". The fair choice would be giving benefits to wares made with green energy, not taxing wares. China didn't get the planets pollution where it is now. We did.
Yes but the alternatives are much easier for a country to afford, understand and build when at a lower tech level (like China compared to the US when old powerplants were build in China for example).
The difference is that taxing something means less people are likely to buy it and when they do we make money, while giving a tax break make the product more competitive while costing us the income we might have had. One is a carrot, the other is a stick. It might not matter on income in the end but it will help push for greener products while taking the high road.
You could prevent a lot more pollution with the same amount of money if the money goes to low hanging fruits in countries with older power infrastructure than trying to tweak something brand new. You don't need to use extra money, just use it smarter. There're lots of ways to finance this smarter if trade wars and nationalism wasn't the top priorities.