1. Agera is a lightweight Android library for reactive programming developed by Google Play Music Team. It uses four interfaces - Observable, Supplier, Receiver, and Updatable to implement the reactive pattern.
2. Repositories are observable objects that supply data and define events as changes to the supplied data. There are simple repositories like static and mutable repositories, and complex repositories that listen to changes in other repositories.
3. Compiled repositories initialize complex repositories in one expression by specifying data sources, processing flow using operators like map and filter, and configurations like error handling. They return reactive sequences to notify subscribers of data changes.