Q: Does Power Data Recovery run in the background, monitoring your files as you create, save or delete them? In other words, will it only recover files that were lost after Power Data Recovery was installed?

The program does not monitor any files. It gets the files by examining the file system (so called on-disk format of the files). There the files are marked with special attributes and names. Recovering is similar: the program scans the hard disk and searches for a special pattern: the stamp of a directory ('.' or '..') and then assumes a lost directory.