1.)Should what is taught in foreign language courses correspond with trends in economics and world power?Up to a point, although it can be taken too far; during the school years of any one person of, say, 18 years old today, they might have started off learning Japanese and German, and now they would be better off learning Mandarin, Sechuan and Cantonese. In five year's time, the "best" (in the sense of most economically useful) language to learn might change again.
On such a basis, people end up knowing too little to be able to speak conversationally, let alone about business.
2.)How can foreign language instruction be drastically improved in America?I don't know how it currently works there, but if it's anything like Britain, I daresay that starting at an earlier age would be the best bet. Anecdotally, I've heard that it's not only easier to learn a language by about age 7, but that once you know two languages fluently, it's a lot easier to learn more.
3.)Will English, the international language of business, be replaced by Chinese?Hard to say right now. China is currently much more interested in selling to the rest of the world than buying from it, and so (like every great trading power that didn't gain pre-eminence through conquest) its people are trying to learn the languages that of the people to whom it is selling. Because of the quirks of world history, those languages are dominated by English.
This is not just because of American dominance, but of historic legacies of British Empire. I won't pursue the idea that American dominance IS a legacy of British Empire, as in present company that might not go down too well

. But, for example, where China is attempting to secure natural mineral resources all over Africa, and the legacy of European colonialism there means that, rather than learning 101 different tribal languages, the Chinese can do business with almost everyone by learning English and French.
So by the time China overtakes America as the world's largest MARKET (as distinct from the largest exporter, in which it hasn't yet overtaken Germany, though it's catching fast), at which point the rest of the world will need to deal with China on China's own terms, chances are enough business people will already know English, and English will be so ingrained on Chinese business culture, that it won't be necessary to learn Mandarin. This is still a long way off.
One thing future Americans
will have to get used to, in this scenario, is hearing foreigners speak "Chinese English" i.e. with a Chinese accent, and some grammatical and linguistic peculiarities. And not just Chinese foreigners, ALL foreigners. Imagine hearing a Mexican or a German speaking English with a strong Chinese accent. Odd, isn't it?
(We Brits have had a similar experience for some time now - most Europeans who learn English speak British English, but every now and again one hears a German or Italian speaking American English, and it just sounds... odd. It's no surprise to hear people from other parts of the world speak American English, but Europeans from "our" backyard sound quite strange.)