What exactly is the "Default" catalog?
The catalog created by default when there is no other catalog.
What is it using as its source?
Nothing until you add items to it.
How can I confirm that it is using the sources I think it should?
Do a search, browse, filter, etc. on it.
Can I safely delete it and just work with a group of separate catalogs?
Yes, absolutely. If you have created your own catalogs, you can delete it.
-Kirk