2) If it rarely changes, why even bother investing in something like this?
http://www.dyndns.org/ If it was changing every 12 hours or something then i would suggest getting something. Other than that no.
3) if your works firewall is blocking alot of the ports so you can access VNC at home there really isnt much you can do. You could try to run VNC on port 80 (internet) and see if that works. Of course if your network admin is smart he/she can see what your doing and they might not like that