Is there some way to setup a user account, such that all directories, besides those within their home directory are invisible and non-navigable from all apps? (symlinks will still give access to the removable drives) Preferred, the user should "feel" as if their home directory is all there is on the computer.

Is this Apache & php ? And will the same restrictions apply to all users? Google/look into 'chroot jail' and php's 'open_basedir()' restriction. If it's not Apache, or this doesn't help, sorry

Try this:
http://olivier.sessink.nl/jailkit/index.html

Problem is you have to allow access (x) to system directories.

You can remove the read if you like unless an application uses readir() in its code and needs to read that directory.

/tmp /var are used by applications to write temporary or variable data, /etc is used to read system wide config details.

You could block out /sbin, /usr/sbin, /boot but they are about the only ones you can do, and /sbin and /usr/sbin can contain binaries a user may wish to use, so more often you find a lot of programs are open to all users.

Now you could chroot but then you will have to make that jail and populate it with /bin /etc etc

Have a look at the FHS and you will see why it is that way.

SELinux though and ACLs may help you more though in fine tuning your system. You don't mention your reason though so we are all shooting a bit blind here.