Have you tried Posts Table Pro for your document library? A lot of people have switched to it after having issues with other document library WordPress plugins. You can add each of your documents as a post or custom post type. The plugin automatically lists all your documents in a table. The table can list any information about each document such as the title, a brief description, file format, file size etc.
This would meet your requirements as follows:
1. Admin users would add each document as a post or custom post, depending on how you decide to structure your documents in the back end.
2) Non-admin users would view the document library on the front end of the website, so they won’t have to make changes. You can add the document library on any page of the website and password protect it using the password protection feature built into WordPress.