I\'d like to fix the cursor to the centre line of the screen, so that when I press Ctrl-N or Ctrl-P, the page itself moves up or down, and the cursor stays still.
Ha
Try centered-cursor mode:
http://www.emacswiki.org/emacs/centered-cursor-mode.el
If you're using MELPA, it's available by M-x package-install RET centered-cursor-mode.
package-install
centered-cursor-mode