Why does China buy so much U.S. Treasury debt? What is the reason that China buys so much US debt in form of Treasuries? How does this help the Chinese economy? It seems they are willing to give money to USA so USA economy can function better (more cash more investing in infrastructure).

What is in it for China, holding a bunch of paper yielding next to nothing?
As was said above, buying debt to affect the exchange rate and make Chinese exports more attractive may be one reason to buy these Treasuries. Surely all of these are not reinvested into buying more debt and some of it is put into other civic projects.

The other reason to buy debt is to have a string of payments over time that may become more valuable later on. Since the US is a large nation and powerful nation, China probably feels it is very unlikely that the USA will default, and if they did, that would give China a legitimate complaint against the US, that might help them in foreign relations. It may even be that they want the US to be stable so as not to crash the global economy and so that they can still sell lots of products to the US, so they buy up the debt to keep the USA stable.

The more important part of that whole paragraph though is to have a string of payments. For the same reason that governments like to hold debt even when they have the ability to pay it off, China might find that investing into debt will provide a better rate of return than infrastructure at the moment, and later on, once infrastructure has a better rate of return (capital steady state changes) then they can take a stream of income from interest payments from the US and taxes and then invest into that.

Finally, I couldn't help but notice that you see China as needing to lift itself out of poverty. That may be true, but why would investments into infrastructure be the solution to helping the rural poor--places that don't need as much infrstructure? Most of the poor in China are in rural areas, so there's something to think about.