Is the ILS CAT III system the most complex landing system available? Is the ILS CAT III the most technologically sophisticated navigation / landing  system available for helping commercial pilots land a commercial passenger aircraft in severe and extremely low visibility weather conditions. Does the airport require special compatible equipment for this system to work properly?
Yes ILS equipment for CATIII is the most sophisticated across ILS systems. As people mentioned in comments there are another types of landing systems, which could be more complex.
No it is not auto landing system.

It self CATIII is a category of a landing conditions.

Also take a look here What is different between a Cat IIIA, Cat IIIB, and Cat IIIC ILS approach?