Zakaria does not think that the Post-American world presents insurmountable problems to America. On the contrary, he states that America will remain as the most powerful nation in the world in the foreseeable future. However, Zakaria acknowledges that due to the rise of the other nations, America’s power has reduced. He further acknowledges the challenges that have resulted from globalization but asserts that America can leverage its remaining power to provide global stability.

There are certain elements of America’s approach that could hinder it from successfully retaining its global leadership. These include any use of “hard power”, hostile immigration policies, general political short-sightedness, and a focus on military dominance, among others. Zakaria proposes that in order to avoid the above, America should relax its immigration policies and strive to be an international arbiter as opposed to focusing on military dominance.

The short answer to this question is no. By "post-American world," Zakaria describes the "rise of the rest," other nations that will become economic powers alongside the United States. While this has led to a great deal of anxiety in the United States, Zakaria emphasizes that it does not mean that the United States will not remain powerful, important, and wealthy.

The "rise of the rest," in short, does not entail the inevitable decline of the United States. Rather, Zakaria views the rise of other nations as an opportunity for the United States. But it will take a sort of paradigm shift on the part of the United States, and Americans, if this is to occur. Americans, in short, have to be willing to abandon their insular outlook and their view, long reinforced by politicians, that the global economy is a zero-sum game.

Despite the growth of economies in China and India, the United States will remain an economic power for the foreseeable future, and it is especially strong in developing innovations, especially technology, that can be marketed to emerging economies. So, Zakaria does not think that the issues posed by the "rise of the rest" are insurmountable, but he emphasizes that the United States must embrace free trade, relatively open immigration policies, and other aspects of a globalized world that will allow it to continue to flourish. 

No, Zakaria does not at all think that the challenges faced by the US are insurmountable.  He is actually fairly optimistic about the US's chances.  The point of the book, in fact, is to argue that a "post-American world" is not one that has to be bad for the US.

What Zakaria thinks is that the US simply needs to be more flexible in a number of ways so that it can benefit from the "rise of the rest."  He thinks the US needs a more flexible attitude towards the world, one in which we do not view the rise of other countries as a threat.  He thinks we need to be flexible in how we see our role in the world.  We need to think of ourselves as a...