Economists don't know what they're talking about

In response to your first question, I think the status of the Austrian School in the academic economic community is quite a bit lower than "out of vogue"; the approach that the Austrian School takes toward the study of economics differs substantially from the mainstream economic community. Modern economics tries very hard to be a "real science"--it creates models, makes predictions, collects data, and sees if the data match the predictions made by the model. And the mainstream academic community has done pretty well with most of this process. The only part they seem to have a lot of trouble with is matching the data to the predictions. Unfortunately, macroeconomic data is influenced by so many factors that it is devilishly difficult to isolate the effect of a single variable. An economist who argues that a variable x has a particular effect will be met with arguments by ten other economists that, no, in fact, the data indicate that it was variables y, z, and omega. Essentially, the mainstream economic community has developed economics into a process of inductive reasoning--collect data and use the data to reason out what's going on.

The Austrians reject this methodology. Because macroeconomic data is influenced by so many different variables (millions of people acting in millions of different ways for millions of different reasons), they claim that it is simply impossible to draw any meaningful conclusions from macroeconomic data--in essence, you see in it whatever you want to see. Instead of inductive reasoning, Austrians turn to deductive reasoning. Thus, Austrians see economics as a subject closer to mathematics than to science. (Though, as I mentioned in my first comment, the Austrians reject mathematical argument as being inadequate to model the complexities of human action; Austrian reasoning is primarily verbal, which draws criticism from the mainstream academic community of being too imprecise to be useful.)

The issue is deeper than the current fashionable theory of economics. In the 1920s and 1930s the Austrian School held a respectable position with mainstream economists. At the time economics was as much deductive as inductive, so the two schools of thought were on equal footing. But as the Keynesians developed their mathematical models, economics became heavily inductive and began to see the Austrian methodology as unscientific. Ever since, various other schools of thought have enjoyed popularity, but the fundamental methodology hasn't changed. Of course, the recent failures of the mainstream economic community to predict this crisis and the success of Peter Schiff in predicting it has brought renewed interest to the Austrian School. I'm not sure, however, that even this will be sufficient to change the fundamental approach taken by the mainstream economic community. As you wrote in your post, "old habits die hard."

In response to your second question, I think that behavioral economics will be useful for the study of human psychology and, to a lesser extent, microeconomics, but I'm not convinced that it will be terribly useful for modeling macroeconomic behavior. Behavorial economics studies what small groups of humans do in very specific laboratory conditions. How well the conclusions from these experiments extend to the real world where millions of humans are doing in a wide variety of conditions is impossible to say--it's just not something that can really be tested.

Chaos theory, similarly, I believe will be quite useful in limited contexts. Chaos theory is very good at telling us what, in general, a system will do over a long time period. But it does not provide much information as to what the system will do at any particular time. More importantly, chaos theory does not shed much light on the question of why the system behaves as it does. In any science, predicting outcomes is important, but it is always secondary to understanding the system. We study science to understand the world; we make predictions to verify that our understanding of the world is correct. At the root of things, understanding why the world works as it does is the important part and chaos theory cannot provide you a priori with that explanation.

For the Austrian School, I think the study of complexity theory might hold some promise. In essence, what Austrian economists have argued since the days of Ludwig von Mises is that the problem of macroeconomic modeling is undecidable. It has (to my knowledge) never been proven, but if it were, it would make a compelling case for the Austrian methodology.