Probably not that problem then. (I was thinking of the root_squash option for NFS, which generally prevents root on the client from being able to do anything useful, in order that someone on J Random machine can't access the entire server simply by claiming to be root. The NFS security model is pretty rudimentary, being designed for a computer lab type environment.)
Network filesystem: There are various ways of mounting filesystems over the network. NFS is traditional, but SMB/CIFS is used by Windows machines, and as such has become well-supported by graphical Linux environments over the years. Also exotica like SSHFS, which is useful over the internet, or for one-off use. Basically, whatever you've put in the third column in /etc/fstab for the mount.
(Not the same thing as the filesystem the server is using internally. Which could be anything, and you don't usually need to care about.)
(Passwords are hashed, so you won't be able to find out what it is, but you can always change the root password by running 'passwd' with sudo. Of course, sudo makes the root password mostly irrelevant. I think it's mostly useful for when something goes horribly wrong to stop the machine booting properly and you need to access single-user mode.)