My question is if there is a way in Lightroom to edit files directly
to disk, without having to re-export again, from the Lightroom
For example, the way Lightroom seems to work now is that it is
creating some kind of an internal library, then Lightroom copies files
into this library, from the disk and sub-folders, and when you are
done making adjustments, you have to export from the library.
I think you have a basic misunderstanding of how Lightroom works. Original files can live on the drive wherever you choose.
Adding a file to the Lightroom library, simply registers that file's path in Lightroom's catalog (which is actually a SQLite database) as an entry. Whenever you edit a file in the Lightroom interface, you're essentially just editing a list of instructions to be run on the file at export. The original file is always left intact, and is never modified after import. Instead, after you've made and saved your changes, those instructions are then run on an exported copy.
This is why Lightroom can create "virtual" copies. It can just create another database record and save a different set of instructions for the same original file, at the same path as if it were a different image in the library. The other big advantage for Lightroom doing things this way is that all edits are non-destructive and undoable, even between sessions. You can quit out of Lightroom, go back, and undo from where you left off.
But because of how Lightroom works, until you export the image you haven't created an edited version of the file.
I am wondering if there is a way to edit files ala perhaps Bridge,
where you can navigate sub-folders.
Lightroom's Library module performs many of the same functions of Bridge, including being able to show the tree-structure of folders and which level you're at, as well as subfolders. How the files are organized is completely up to you and how you import files. You can manually rearrange things all you want in the Library module, and you will actually be manipulating where files live on the hard drive. The main difference between dragging in the Library module, and dragging using your operating system's file organizing windows is that whatever change you make in the Library module will also be updated in the Lightroom catalog (SQLite database). If you move files outside of Lightroom, the database records will have outdated file paths, and will notify you that they need to be corrected the next time you try to access the file.