Short answers, pulled from the story.
Lucas received the Nobel Memorial Prize in Economic Sciences in 1995 for developing and applying the hypothesis of rational expectations, which transformed macroeconomic analysis and deepened understanding of economic policy. The Nobel citation used those exact words to describe his contribution.
The Lucas critique, formulated in 1976, argues that the relationships economists observe between economic variables, such as inflation and unemployment, are not fixed laws but depend on the prevailing policy regime. When policymakers try to exploit an observed correlation, the correlation itself tends to break down, making predictions based on historical patterns unreliable.
In 2003, approximately five years before the Great Recession, Lucas stated that the central problem of depression-prevention had been solved for all practical purposes and had in fact been solved for many decades. The subsequent financial crisis made that statement one of the most scrutinized claims in modern macroeconomics.
The Lucas paradox is the observation that capital does not flow as freely from rich countries to poor countries as standard economic theory would predict. Since capital should earn higher returns where it is scarce, the theory implies large flows to developing economies, but the observed pattern falls well short of that prediction.
Yes. Lucas's divorce settlement with his first wife, Rita Cohen, included a clause entitling her to half of any Nobel Prize winnings if the prize was awarded before the 31st of October 1995. The Nobel Committee announced the award that year within the deadline, and Cohen received her share.
Lucas spent the bulk of his career at the University of Chicago, where he earned his PhD in economics in 1964 and to which he returned permanently in 1975 after teaching at the Graduate School of Industrial Administration at Carnegie Mellon University from the time of his graduation.