The “Manage Files” screen will only show files that are attached to sermons. For all other files, you’ll need to use the “Media > Library” screen.
You can filter sermon files by Preacher, Series, and Service (will look slightly different on different screens):
Like the default WordPress Media Library, hovering over the file exposes the links:
Selecting “Edit Sermon” will take you to the sermon editor. You can acquire the direct link to the file here, and (if your theme supports it) you can link to the files unique page. (Here is more information on attachment pages.)
To rename the file, or check MP3 tags, or other useful things, click “Edit File”. If the file is an MP3, you’ll get this screen:
If your MP3 has valid IDv2 or IDv1 tags, they will show up here. You can edit the title, description, date, file name, and slug easily enough.
Planned feature: Edit MP3 tags, set Album Art.
The sermon file can be given a custom thumbnail, or “Featured” image, which can be used in templates if desired. Clicking on the “Add/Edit Featured Image” button will pop up the familiar display.
Planned Feature: Upload image from URL. (Tab is there, but does not work.)

