Does it need a web server or a database?

No. It serves HTTPS itself and keeps its metadata in SQLite. It works behind a reverse proxy if you already have one, but does not require it.

Where do the files actually live?

On disk, in ordinary folders, under the storage directory you choose. If the program disappeared tomorrow, the files would still be readable with a file manager.

Can users register themselves?

No, and that is deliberate. The administrator creates accounts. A file server with open registration is a file server that fills with strangers.

What happens to deleted files?

They go to the trash and can be restored to their previous place in one click. The retention period is configurable, and the trash can be switched off entirely if you prefer deletion to be final.