Q. Where can I find information on annual production rate of various products by different countries?

Many governments publish this sort of information online, which means you'll want to get familiar with official government URLs and a bit of advanced searching in your search engine of choice.

Using Google as an example: Looking for the annual production rate of corn syrup in the United States? We know American governmental website URLs end in .gov, so searching "annual corn syrup production site:.gov" will search only websites that end in .gov, which will give you more reliable results than searching everything on the web.