Economic impacts of a declining population
ad 2. 
This phenomenon has been studied a lot. Broadly it is referred to as the demographic transition. A good overview is given by the respective Wikipedia article.

In the field of Long-term macro there are several publications. One of the latest top-journal publications is:
Cervellati M.; Sunde U., Life Expectancy and Economic Growth: The Role of The Demographic Transition, «JOURNAL OF ECONOMIC GROWTH», 2011, 16(2), pp. 99 - 133.

Demographic elements can for sure be endogenised into every macro model. But I doubt that it would be very useful for short run DSGE things, since all demographic changes take place with huge time lags. If you want to study those interesting phenomena, you probably have to go more into Long-run Macro / Economic Growth (Unified Growth Theories put emphasis on demographic elements for instance)