I saved my FirstLight project for a set of media files after configuring them how I wanted--however when opening the FirstLight project again, all the files are gone from the media bin and when I drag them back into the bin or re-import them, all my configurations are gone. What's the point of saving a FirstLight project file? What is it saving exactly?

FirstLight project is just a file list, not configuration data (Active Metadata) is stored in the project (that wouldn't be a good idea -- but complex to explain way.) The A.M. is stored in folder pointed to by the registry.

The default location is
C:\Users\Public\CineForm\LUTs\db

'db' is the current name of your database.

So like you corrections are no lost, rather you changed the default database path or database name accidentally.

I move my default location into Dropbox so my corrections are automatically shared with all my system (home and work.) See vimeo video on how to do this: CineForm FirstLight color correction through Dropbox on Vimeo