It converts your regexp into a virtual filesystem and then you can test if a string matches the regexp by converting the string into a path and testing if that path is contained in the filesystem.
I wouldn't necessarily call this useful for anything in particular. It's more of a silly trick to show off than anything. (And a reminder of how regexes work behind the scenes.)
That wouldn’t work. This works by hard linking a lot of directories to each other, so if you were to write a file there, it ends up in multiple locations (possibly all ‘directories’ in the file system)
The file system could work around that by creating new unique directories whenever you write any file to an empty directory, but that would require it to keep the regular expression it represents around, and would fill up the file system quite rapidly.